Question 1

Assume that the expressions given are denominators of fractions. Find the least common denominator.
-$x^{2}-5 x+6, x^{2}-8 x+12$

Accepted Answer

A)  $(x-2)(x-6)$ 
B)  $(x-3)(x-2)(x-6)$ 
C)  $(x-3)(x-2)$ 
D)  $(x+3)(x+2)(x-6)$ 
A)  $(x-2)(x-6)$ 
B)  $(x-3)(x-2)(x-6)$ 
C)  $(x-3)(x-2)$ 
D)  $(x+3)(x+2)(x-6)$

Question 2

Martha can rake the leaves in her yard in 4 hours. Her younger brother can do the job in 7 hours. How long will it take them to do the job if they work together?

Accepted Answer

A)  $7 \mathrm{hr}$ 
B)  $\frac{28}{3} \mathrm{hr}$ 
C)  $\frac{11}{28} \mathrm{hr}$ 
D)  $\frac{28}{11} \mathrm{hr}$ 
A)  $7 \mathrm{hr}$ 
B)  $\frac{28}{3} \mathrm{hr}$ 
C)  $\frac{11}{28} \mathrm{hr}$ 
D)  $\frac{28}{11} \mathrm{hr}$

Question 3

Express the rational expression in lowest terms.
-$\frac{4 x+2}{20 x^{2}+22 x+6}$

Accepted Answer

A)  $\frac{4 x}{5 x+3}$ 
B)  $\frac{4 x+5}{5 x+22}$ 
C)  $\frac{4 x+2}{20 x^{2}+22 x+6}$ 
D)  $\frac{1}{5 x+3}$ 
A)  $\frac{4 x}{5 x+3}$ 
B)  $\frac{4 x+5}{5 x+22}$ 
C)  $\frac{4 x+2}{20 x^{2}+22 x+6}$ 
D)  $\frac{1}{5 x+3}$

Question 4

Perform the indicated operation and express in lowest terms.
-$\frac{16 s^{2}+8 s t+t^{2}}{2 s^{2}-9 s t-5 t^{2}} \cdot \frac{2 s^{2}-11 s t+5 t^{2}}{t^{2}+3 s t-4 s^{2}} \div \frac{8 s^{2}-2 s t-t^{2}}{2 s^{2}+3 s t+t^{2}}$

Accepted Answer

A)  $\frac{t+s}{t-s}$ 
B)  $\frac{(\mathrm{t}+4 \mathrm{~s})}{(\mathrm{t}+\mathrm{s})(\mathrm{t}-\mathrm{s})}$ 
C)  1 
D)  $\frac{(t+4 x)^{2}(2 x-t)^{2}}{(4 s+t)^{2}\left(t^{2}-s^{2}\right)}$ 
A)  $\frac{t+s}{t-s}$ 
B)  $\frac{(\mathrm{t}+4 \mathrm{~s})}{(\mathrm{t}+\mathrm{s})(\mathrm{t}-\mathrm{s})}$ 
C)  1 
D)  $\frac{(t+4 x)^{2}(2 x-t)^{2}}{(4 s+t)^{2}\left(t^{2}-s^{2}\right)}$

Question 5

An experienced accountant can balance the books twice as fast as a new accountant. Working together it takes the accountants 8 hours. How long would it take the experienced accountant working alone?

Accepted Answer

A)  $16 \mathrm{hr}$ 
B)  $4 \mathrm{hr}$ 
C)  $20 \mathrm{hr}$ 
D)  $12 \mathrm{hr}$ 
A)  $16 \mathrm{hr}$ 
B)  $4 \mathrm{hr}$ 
C)  $20 \mathrm{hr}$ 
D)  $12 \mathrm{hr}$

Question 6

The resistance, in ohms, of a 25 -foot piece of wire is given by the function $R(d)=\frac{0.025}{d^{2}}$, where $d$ is the diameter of the wire in inches. What is the resistance, rounded to the nearest hundredth of an $\mathrm{ohm}$, if the wire has a diameter of 0.05 inches?

Accepted Answer

A)  $15.67 \mathrm{ohms}$ 
B)  $9.66 \mathrm{ohms}$ 
C)  $10.12 \mathrm{ohms}$ 
D)  $10.00 \mathrm{ohms}$ 
A)  $15.67 \mathrm{ohms}$ 
B)  $9.66 \mathrm{ohms}$ 
C)  $10.12 \mathrm{ohms}$ 
D)  $10.00 \mathrm{ohms}$

Question 7

Tell whether or not the rational expressions are equivalent.
-$\frac{4 \mathrm{~m}^{5}}{8}, \frac{\mathrm{m}^{5}}{4}$

Accepted Answer

A) True 
 B)False

Question 8

Perform the indicated operation and express in lowest terms.
-$\frac{3 x^{2}(x-2 y)-22 x(x-2 y)+7(x-2 y)}{3 x^{2}(2 y-x)-20 x(2 y-x)-7(2 y-x)} \div \frac{4 x-1}{3 x+1}$

Accepted Answer

A)  $\frac{3 x+1}{x-7}$ 
B)  $-\frac{3 x+1}{4 x-5}$ 
C)  1 
D)  $-\frac{3 x-1}{4 x-1}$ 
A)  $\frac{3 x+1}{x-7}$ 
B)  $-\frac{3 x+1}{4 x-5}$ 
C)  1 
D)  $-\frac{3 x-1}{4 x-1}$

Question 9

Solve the formula for the specified variable.
-$F=\frac{9}{5} C+32$ for $C$

Accepted Answer

A)  $C=\frac{9}{5}(\mathrm{~F}-32)$ 
B)  $C=\frac{F-32}{9}$ 
C)  $C=\frac{5}{F-32}$ 
D)  $C=\frac{5}{9}(F-32)$ 
A)  $C=\frac{9}{5}(\mathrm{~F}-32)$ 
B)  $C=\frac{F-32}{9}$ 
C)  $C=\frac{5}{F-32}$ 
D)  $C=\frac{5}{9}(F-32)$

Question 10

Assume that the expressions given are denominators of fractions. Find the least common denominator.
-$15 x y, 6 x^{2}$

Accepted Answer

A)  $30 x^{2} y$ 
B)  $30 x y^{2}$ 
C)  $30 x y^{3}$ 
D)  $30 x^{3} y$ 
A)  $30 x^{2} y$ 
B)  $30 x y^{2}$ 
C)  $30 x y^{3}$ 
D)  $30 x^{3} y$

Question 11

The average number of vehicles waiting in line at a toll booth of a super highway is modeled by the function $n(x)=\frac{x^{2}}{0.5(1-x)}$, where $x$ is a quantity between 0 and 1 known as the traffic intensity.
What happens to the average number of vehicles waiting as traffic intensity increases?

Accepted Answer

A)  The average number of vehicles waiting increases. 
B)  The average number of vehicles waiting decreases at first, but then increases. 
C)  The average number of vehicles waiting decreases. 
D)  The average number of vehicles waiting remains constant. 
A)  The average number of vehicles waiting increases. 
B)  The average number of vehicles waiting decreases at first, but then increases. 
C)  The average number of vehicles waiting decreases. 
D)  The average number of vehicles waiting remains constant.

Question 12

Use two different methods to simplify the fraction. Explain each step of your work.
$$\frac{\frac{15}{p}-\frac{25}{m}}{\frac{30}{p}+\frac{10}{m}}$$

Accepted Answer

One method is to simplify the numerator

Question 13

Add or subtract as indicated.
-$\frac{8}{x-2}-\frac{x}{x-5}+\frac{x^{2}+40}{x^{2}-7 x+10}$

Accepted Answer

A)  $\frac{2 x^{2}+6 x-80}{(x+2)(x+5)}$ 
B)  $\frac{10 x}{(x+2)(x+5)}$ 
C)  $\frac{6 x}{(x-2)(x-5)}$ 
D)  $\frac{10 x}{(x-2)(x-5)}$ 
A)  $\frac{2 x^{2}+6 x-80}{(x+2)(x+5)}$ 
B)  $\frac{10 x}{(x+2)(x+5)}$ 
C)  $\frac{6 x}{(x-2)(x-5)}$ 
D)  $\frac{10 x}{(x-2)(x-5)}$

Question 14

Find all numbers that are not in the domain of the function. Then give the domain using set notation.
-$f(x)=\frac{2 x+22}{x^{2}-1}$

Accepted Answer

A)  $1 ;\{x \mid x \neq 1\}$ 
B)  none; $(\infty, \infty)$ 
C)  $-1,1 ;\{x \mid x \neq-1,1\}$ 
D)  $-11,-1,1 ;\{x \mid x \neq-11,-1,1\}$ 
A)  $1 ;\{x \mid x \neq 1\}$ 
B)  none; $(\infty, \infty)$ 
C)  $-1,1 ;\{x \mid x \neq-1,1\}$ 
D)  $-11,-1,1 ;\{x \mid x \neq-11,-1,1\}$

Question 15

Perform the indicated operation and express in lowest terms.
-$\frac{13}{7 x^{2}}-\frac{11}{7 x^{2}}$

Accepted Answer

A)  $\frac{2}{14 x^{4}}$ 
B)  $\frac{7}{2 x^{2}}$ 
C)  2 
D)  $\frac{2}{7 x^{2}}$ 
A)  $\frac{2}{14 x^{4}}$ 
B)  $\frac{7}{2 x^{2}}$ 
C)  2 
D)  $\frac{2}{7 x^{2}}$

Question 16

Graph the rational function. Give the equations of the vertical and horizontal asymptotes.
-$f(x)=\frac{1}{x+2}$

Accepted Answer

A)  $x=2 ; y=0$
  
B) $ x = 0; y = -2$
  
C)  $ x = 0; y = 2$
  
D)  $x=-2 ; y=0$
  
A)  $x=2 ; y=0$
  
B) $ x = 0; y = -2$
  
C)  $ x = 0; y = 2$
  
D)  $x=-2 ; y=0$

Question 17

Tell whether or not the rational expressions are equivalent.
-$\frac{(3-m)(4-n)}{(m-3)(4+n)}, \frac{3-m}{m+3}$

Accepted Answer

A) True 
 B)False

Question 18

Choose the one alternative that best completes the statement or answers the question.
-The volume of wood in a tree varies jointly as the height of the tree and the square of the distance around the tree trunk. If the volume of wood is 15.84 cubic feet when the height is 22 feet and the distance around the trunk is 3 feet, what is the volume of wood obtained from a tree that is 35 feet tall having a measurement of 4 feet around the trunk?

Accepted Answer

A)  $48.8 \mathrm{ft}^{3}$ 
B)  $53.8 \mathrm{ft}^{3}$ 
C)  $44.8 \mathrm{ft}^{3}$ 
D)  $36.8 \mathrm{ft}^{3}$ 
A)  $48.8 \mathrm{ft}^{3}$ 
B)  $53.8 \mathrm{ft}^{3}$ 
C)  $44.8 \mathrm{ft}^{3}$ 
D)  $36.8 \mathrm{ft}^{3}$

Question 19

Is $\frac{s^{-1}+z^{-1}}{s^{-4}-z^{-4}}=\frac{s-z}{s+z}$ a true statement? Explain your answer by simplifying the expression on the left, step by step, until it is an expression with only positive exponents that cannot be further simplified.

Accepted Answer

No, it is not a true

Question 20

Choose the one alternative that best completes the statement or answers the question.
-The current $I$ in an electrical conductor varies inversely as the resistance $R$ of the conductor. The current is 6 amperes when the resistance is 894 ohms. What is the current when the resistance is 736 ohms?

Accepted Answer

A)  $4.9 \mathrm{amps}$ 
B)  $0.14 \mathrm{amps}$ 
C)  $0.2 \mathrm{amps}$ 
D)  $7.3 \mathrm{amps}$ 
A)  $4.9 \mathrm{amps}$ 
B)  $0.14 \mathrm{amps}$ 
C)  $0.2 \mathrm{amps}$ 
D)  $7.3 \mathrm{amps}$

Assume that the expressions given are denominators of fractions. Find the least common denominator. - $x^{2}-5 x+6, x^{2}-8 x+12$

Martha can rake the leaves in her yard in 4 hours. Her younger brother can do the job in 7 hours. How long will it take them to do the job if they work together?

Express the rational expression in lowest terms. - $\frac{4 x+2}{20 x^{2}+22 x+6}$

Perform the indicated operation and express in lowest terms. - $\frac{16 s^{2}+8 s t+t^{2}}{2 s^{2}-9 s t-5 t^{2}} \cdot \frac{2 s^{2}-11 s t+5 t^{2}}{t^{2}+3 s t-4 s^{2}} \div \frac{8 s^{2}-2 s t-t^{2}}{2 s^{2}+3 s t+t^{2}}$

An experienced accountant can balance the books twice as fast as a new accountant. Working together it takes the accountants 8 hours. How long would it take the experienced accountant working alone?

The resistance, in ohms, of a 25 -foot piece of wire is given by the function $R(d)=\frac{0.025}{d^{2}}$ , where $d$ is the diameter of the wire in inches. What is the resistance, rounded to the nearest hundredth of an $\mathrm{ohm}$ , if the wire has a diameter of 0.05 inches?

Tell whether or not the rational expressions are equivalent. - $\frac{4 \mathrm{~m}^{5}}{8}, \frac{\mathrm{m}^{5}}{4}$

Perform the indicated operation and express in lowest terms. - $\frac{3 x^{2}(x-2 y)-22 x(x-2 y)+7(x-2 y)}{3 x^{2}(2 y-x)-20 x(2 y-x)-7(2 y-x)} \div \frac{4 x-1}{3 x+1}$

Solve the formula for the specified variable. - $F=\frac{9}{5} C+32$ for $C$

Assume that the expressions given are denominators of fractions. Find the least common denominator. - $15 x y, 6 x^{2}$

The average number of vehicles waiting in line at a toll booth of a super highway is modeled by the function $n(x)=\frac{x^{2}}{0.5(1-x)}$ , where $x$ is a quantity between 0 and 1 known as the traffic intensity. What happens to the average number of vehicles waiting as traffic intensity increases?

Use two different methods to simplify the fraction. Explain each step of your work. $\frac{\frac{15}{p}-\frac{25}{m}}{\frac{30}{p}+\frac{10}{m}}$

Add or subtract as indicated. - $\frac{8}{x-2}-\frac{x}{x-5}+\frac{x^{2}+40}{x^{2}-7 x+10}$

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - $f(x)=\frac{2 x+22}{x^{2}-1}$

Perform the indicated operation and express in lowest terms. - $\frac{13}{7 x^{2}}-\frac{11}{7 x^{2}}$

Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - $f(x)=\frac{1}{x+2}$ $Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - f(x)=\frac{1}{x+2}$

Tell whether or not the rational expressions are equivalent. - $\frac{(3-m)(4-n)}{(m-3)(4+n)}, \frac{3-m}{m+3}$

Is $\frac{s^{-1}+z^{-1}}{s^{-4}-z^{-4}}=\frac{s-z}{s+z}$ a true statement? Explain your answer by simplifying the expression on the left, step by step, until it is an expression with only positive exponents that cannot be further simplified.

Choose the one alternative that best completes the statement or answers the question. -The current $I$ in an electrical conductor varies inversely as the resistance $R$ of the conductor. The current is 6 amperes when the resistance is 894 ohms. What is the current when the resistance is 736 ohms?

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 7: Rational Expressions and Functions

Assume that the expressions given are denominators of fractions. Find the least common denominator. - x2−5x+6,x2−8x+12x^{2}-5 x+6, x^{2}-8 x+12x2−5x+6,x2−8x+12

Martha can rake the leaves in her yard in 4 hours. Her younger brother can do the job in 7 hours. How long will it take them to do the job if they work together?

Express the rational expression in lowest terms. - 4x+220x2+22x+6\frac{4 x+2}{20 x^{2}+22 x+6}20x2+22x+64x+2​

An experienced accountant can balance the books twice as fast as a new accountant. Working together it takes the accountants 8 hours. How long would it take the experienced accountant working alone?

Tell whether or not the rational expressions are equivalent. - 4 m58,m54\frac{4 \mathrm{~m}^{5}}{8}, \frac{\mathrm{m}^{5}}{4}84 m5​,4m5​

Solve the formula for the specified variable. - F=95C+32F=\frac{9}{5} C+32F=59​C+32 for CCC

Assume that the expressions given are denominators of fractions. Find the least common denominator. - 15xy,6x215 x y, 6 x^{2}15xy,6x2

Use two different methods to simplify the fraction. Explain each step of your work. 15p−25m30p+10m\frac{\frac{15}{p}-\frac{25}{m}}{\frac{30}{p}+\frac{10}{m}}p30​+m10​p15​−m25​​

Add or subtract as indicated. - 8x−2−xx−5+x2+40x2−7x+10\frac{8}{x-2}-\frac{x}{x-5}+\frac{x^{2}+40}{x^{2}-7 x+10}x−28​−x−5x​+x2−7x+10x2+40​

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - f(x)=2x+22x2−1f(x)=\frac{2 x+22}{x^{2}-1}f(x)=x2−12x+22​

Perform the indicated operation and express in lowest terms. - 137x2−117x2\frac{13}{7 x^{2}}-\frac{11}{7 x^{2}}7x213​−7x211​

Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - f(x)=1x+2f(x)=\frac{1}{x+2}f(x)=x+21​

Tell whether or not the rational expressions are equivalent. - (3−m)(4−n)(m−3)(4+n),3−mm+3\frac{(3-m)(4-n)}{(m-3)(4+n)}, \frac{3-m}{m+3}(m−3)(4+n)(3−m)(4−n)​,m+33−m​

Choose the one alternative that best completes the statement or answers the question. -The current III in an electrical conductor varies inversely as the resistance RRR of the conductor. The current is 6 amperes when the resistance is 894 ohms. What is the current when the resistance is 736 ohms?

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Assume that the expressions given are denominators of fractions. Find the least common denominator. - $x^{2}-5 x+6, x^{2}-8 x+12$

Express the rational expression in lowest terms. - $\frac{4 x+2}{20 x^{2}+22 x+6}$

Tell whether or not the rational expressions are equivalent. - $\frac{4 \mathrm{~m}^{5}}{8}, \frac{\mathrm{m}^{5}}{4}$

Solve the formula for the specified variable. - $F=\frac{9}{5} C+32$ for $C$

Assume that the expressions given are denominators of fractions. Find the least common denominator. - $15 x y, 6 x^{2}$

Use two different methods to simplify the fraction. Explain each step of your work. $\frac{\frac{15}{p}-\frac{25}{m}}{\frac{30}{p}+\frac{10}{m}}$

Add or subtract as indicated. - $\frac{8}{x-2}-\frac{x}{x-5}+\frac{x^{2}+40}{x^{2}-7 x+10}$

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - $f(x)=\frac{2 x+22}{x^{2}-1}$

Perform the indicated operation and express in lowest terms. - $\frac{13}{7 x^{2}}-\frac{11}{7 x^{2}}$

Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - $f(x)=\frac{1}{x+2}$ $Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - f(x)=\frac{1}{x+2}$

Tell whether or not the rational expressions are equivalent. - $\frac{(3-m)(4-n)}{(m-3)(4+n)}, \frac{3-m}{m+3}$

Choose the one alternative that best completes the statement or answers the question. -The current $I$ in an electrical conductor varies inversely as the resistance $R$ of the conductor. The current is 6 amperes when the resistance is 894 ohms. What is the current when the resistance is 736 ohms?