Question 1

Perform the indicated operation and express in lowest terms.
-$\frac{(2 x-5)(x+2)}{(x+9)(x-3)} \div \frac{(x+2)(3 x+5)}{(x+9)(x-3)}$

Accepted Answer

A)  $-\frac{2 x-5}{3 x+5}$ 
B)  $\frac{x-9}{x+2}$ 
C)  $\frac{2 x-5}{3 x+5}$ 
D)  $\frac{2}{3}$ 
A)  $-\frac{2 x-5}{3 x+5}$ 
B)  $\frac{x-9}{x+2}$ 
C)  $\frac{2 x-5}{3 x+5}$ 
D)  $\frac{2}{3}$

Question 2

The current, in amperes, for a piece of wire with an electromotive force of 82 volts, is given by the function $C(r)=\frac{82}{r}$, where $r$ is the resistance of the wire in ohms. What is the current, rounded to the nearest hundredth of an ampere, if the wire has a resistance of 16 ohms?

Accepted Answer

A)  5.06 amperes 
B)  5.37 amperes 
C)  51.25 amperes 
D)  5.13 amperes 
A)  5.06 amperes 
B)  5.37 amperes 
C)  51.25 amperes 
D)  5.13 amperes

Question 3

Are the two expressions equivalent? If so, explain your answer. If not, choose values for $x$ and $p$ as a counter-example.
$\frac{1}{x}-\frac{1}{p}$ and $\frac{1}{x-p}$

Accepted Answer

The expressions are

Question 4

Tell whether or not the rational expressions are equivalent.
-$\frac{18 x^{2} y^{4}}{36 x^{3} y^{2}}, \frac{2 y^{2}}{4 x}$

Accepted Answer

A) True 
 B)False

Question 5

Find all numbers that are not in the domain of the function. Then give the domain using set notation.
-$f(x)=\frac{x+1}{3 x+4}$

Accepted Answer

A)  $-\frac{4}{3} ;\left\{\left\{x \mid x \neq-\frac{4}{3}\right\}\right.$ 
B)  none; $(\infty, \infty)$ 
C)  $-\frac{4}{3},-1 ;\left\{x \mid x \neq-\frac{4}{3},-1\right\}$ 
D)  $\frac{4}{3} ;\left\{x \mid x \neq \frac{4}{3}\right\}$ 
A)  $-\frac{4}{3} ;\left\{\left\{x \mid x \neq-\frac{4}{3}\right\}\right.$ 
B)  none; $(\infty, \infty)$ 
C)  $-\frac{4}{3},-1 ;\left\{x \mid x \neq-\frac{4}{3},-1\right\}$ 
D)  $\frac{4}{3} ;\left\{x \mid x \neq \frac{4}{3}\right\}$

Question 6

Solve the problem. Round your answer, as needed.
-On a map of the United States, the distance between Phoenix and Reno is 2.4 inches. The two cities are actually 768 miles apart. On this same map, what would be the distance between two cities that are 1216 miles apart?

Accepted Answer

A)  3.7 inches 
B)  3.8 inches 
C)  4.1 inches 
D)  3.9 inches 
A)  3.7 inches 
B)  3.8 inches 
C)  4.1 inches 
D)  3.9 inches

Question 7

Tell whether or not the rational expressions are equivalent.
-$\frac{x^{2}(x+1)}{x(x-1)}, \frac{x(x+1)}{x-1}$

Accepted Answer

A) True 
 B)False

Question 8

$1-\frac{3}{2 x}=\frac{7}{4}$

Accepted Answer

A)  $\{2\}$ 
B)  $\left\{-\frac{1}{2}\right\}$ 
C)  $\left\{\frac{1}{2}\right\}$ 
D)  $\{-2\}$ 
A)  $\{2\}$ 
B)  $\left\{-\frac{1}{2}\right\}$ 
C)  $\left\{\frac{1}{2}\right\}$ 
D)  $\{-2\}$

Question 9

$\frac{1}{w+11}+\frac{1}{3 w-8}=\frac{-41}{3 w^{2}+25 w-88}$

Accepted Answer

A)  $\left\{\frac{8}{3},-11\right\}$ 
B)  $\{-11\}$ 
C)  $\{-3\}$ 
D)  $\varnothing$ 
A)  $\left\{\frac{8}{3},-11\right\}$ 
B)  $\{-11\}$ 
C)  $\{-3\}$ 
D)  $\varnothing$

Question 10

Choose the one alternative that best completes the statement or answers the question.
Determine whether the variation between the indicated quantities is direct or inverse.
-The time it takes to drive 100 miles and the speed at which you drive

Accepted Answer

A)  Inverse 
B)  Direct 
A)  Inverse 
B)  Direct

Question 11

Find all numbers that are not in the domain of the function. Then give the domain using set notation.
-$f(x)=\frac{x-3}{8}$

Accepted Answer

A)  $8 ;\{x \mid x \neq 8\}$ 
B)  $0 ;\{x \mid x \neq 0\}$ 
C)  $3 ;\{x \mid x \neq 3\}$ 
D)  none; $(-\infty, \infty)$ 
A)  $8 ;\{x \mid x \neq 8\}$ 
B)  $0 ;\{x \mid x \neq 0\}$ 
C)  $3 ;\{x \mid x \neq 3\}$ 
D)  none; $(-\infty, \infty)$

Question 12

Perform the indicated operation and express in lowest terms.
-$\frac{16}{19 x}-\frac{8}{19 x}$

Accepted Answer

A)  $\frac{19 x}{8}$ 
B)  $\frac{8}{38 x}$ 
C)  $\frac{8}{19 x}$ 
D)  8 
A)  $\frac{19 x}{8}$ 
B)  $\frac{8}{38 x}$ 
C)  $\frac{8}{19 x}$ 
D)  8

Question 13

One maid can clean the house three times faster than another. Working together they can clean the entire house in 3 hours. How long would it take the faster maid cleaning alone?

Accepted Answer

A)  $\frac{3}{4} \mathrm{hr}$ 
B)  $4 \mathrm{hr}$ 
C)  $5 \mathrm{hr}$ 
D)  $3 \mathrm{hr}$ 
A)  $\frac{3}{4} \mathrm{hr}$ 
B)  $4 \mathrm{hr}$ 
C)  $5 \mathrm{hr}$ 
D)  $3 \mathrm{hr}$

Question 14

Find the requested expression for the function.
-If $x$ represents the size of the order to replenish an inventory of computers, then the annual inventory cost is given by the function $c(x)=\frac{2,000,000}{x}+\frac{73}{10}$. Simplify the expression for $c(x)$ by performing the indicated addition.

Accepted Answer

A)  $c(x)=\frac{20,000,000+73 x}{5 x}$ 
B)  $c(x)=\frac{2,000,073}{10 x}$ 
C)  $c(x)=\frac{2,000,000+73 x}{x}$ 
D)  $c(x)=\frac{20,000,000+73 x}{10 x}$ 
A)  $c(x)=\frac{20,000,000+73 x}{5 x}$ 
B)  $c(x)=\frac{2,000,073}{10 x}$ 
C)  $c(x)=\frac{2,000,000+73 x}{x}$ 
D)  $c(x)=\frac{20,000,000+73 x}{10 x}$

Question 15

Express the rational expression in lowest terms.
-$\frac{y^{2}-3 y-18}{y^{2}+2 y-48}$

Accepted Answer

A)  $-\frac{y^{2}-3 y-18}{y^{2}+2 y-48}$ 
B)  $\frac{-3 y-3}{2 y-8}$ 
C)  $\frac{-3 y-18}{2 y-48}$ 
D)  $\frac{y+3}{y+8}$ 
A)  $-\frac{y^{2}-3 y-18}{y^{2}+2 y-48}$ 
B)  $\frac{-3 y-3}{2 y-8}$ 
C)  $\frac{-3 y-18}{2 y-48}$ 
D)  $\frac{y+3}{y+8}$

Question 16

Suppose the triangles shown are similar, with angle $A=$ angle $D$, angle $B=$ angle $E$, and angle $C=$ angle $F$. Answer the question.
- 
What is the length of side DF?

Accepted Answer

A)  22 
B)  24 
C)  48 
D)  32 
A)  22 
B)  24 
C)  48 
D)  32

Question 17

Choose the one alternative that best completes the statement or answers the question.
Determine whether the variation between the indicated quantities is direct or inverse.
-The price of an item and the quantity of the item that you can purchase with a given amount of money

Accepted Answer

A)  Inverse 
B)  Direct 
A)  Inverse 
B)  Direct

Question 18

Write the rational expression in lowest terms.
-$\frac{(y-3)(y-5)}{(5-y)(3+y)}$

Accepted Answer

A)  $\frac{-(3+y)}{(3+y)}$ 
B)  $\frac{3-y}{3+y}$ 
C)  -1 
D)  $\frac{(-y-3)}{(3+y)}$ 
A)  $\frac{-(3+y)}{(3+y)}$ 
B)  $\frac{3-y}{3+y}$ 
C)  -1 
D)  $\frac{(-y-3)}{(3+y)}$

Question 19

Use two different methods to simplify the fraction. Explain each step of your work.
$$\frac{z-\frac{z+4}{24}}{\frac{5}{6}+\frac{7}{4 z}}$$

Accepted Answer

One method is to simplify the numerator

Question 20

Perform the indicated operation and express in lowest terms.
-$\frac{2 p-2}{p} \div \frac{5 p-5}{7 p^{2}}$

Accepted Answer

A)  $\frac{14 p^{3}-14 p^{2}}{5 p^{2}-5 p}$ 
B)  $\frac{14 p}{5}$ 
C)  $\frac{10 p^{2}+20 p+10}{7 p^{3}}$ 
D)  $\frac{5}{14 p}$ 
A)  $\frac{14 p^{3}-14 p^{2}}{5 p^{2}-5 p}$ 
B)  $\frac{14 p}{5}$ 
C)  $\frac{10 p^{2}+20 p+10}{7 p^{3}}$ 
D)  $\frac{5}{14 p}$

Perform the indicated operation and express in lowest terms. - $\frac{(2 x-5)(x+2)}{(x+9)(x-3)} \div \frac{(x+2)(3 x+5)}{(x+9)(x-3)}$

The current, in amperes, for a piece of wire with an electromotive force of 82 volts, is given by the function $C(r)=\frac{82}{r}$ , where $r$ is the resistance of the wire in ohms. What is the current, rounded to the nearest hundredth of an ampere, if the wire has a resistance of 16 ohms?

Are the two expressions equivalent? If so, explain your answer. If not, choose values for $x$ and $p$ as a counter-example. $\frac{1}{x}-\frac{1}{p}$ and $\frac{1}{x-p}$

Tell whether or not the rational expressions are equivalent. - $\frac{18 x^{2} y^{4}}{36 x^{3} y^{2}}, \frac{2 y^{2}}{4 x}$

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - $f(x)=\frac{x+1}{3 x+4}$

Solve the problem. Round your answer, as needed. -On a map of the United States, the distance between Phoenix and Reno is 2.4 inches. The two cities are actually 768 miles apart. On this same map, what would be the distance between two cities that are 1216 miles apart?

Tell whether or not the rational expressions are equivalent. - $\frac{x^{2}(x+1)}{x(x-1)}, \frac{x(x+1)}{x-1}$

$1-\frac{3}{2 x}=\frac{7}{4}$

$\frac{1}{w+11}+\frac{1}{3 w-8}=\frac{-41}{3 w^{2}+25 w-88}$

Choose the one alternative that best completes the statement or answers the question. Determine whether the variation between the indicated quantities is direct or inverse. -The time it takes to drive 100 miles and the speed at which you drive

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - $f(x)=\frac{x-3}{8}$

Perform the indicated operation and express in lowest terms. - $\frac{16}{19 x}-\frac{8}{19 x}$

One maid can clean the house three times faster than another. Working together they can clean the entire house in 3 hours. How long would it take the faster maid cleaning alone?

Find the requested expression for the function. -If $x$ represents the size of the order to replenish an inventory of computers, then the annual inventory cost is given by the function $c(x)=\frac{2,000,000}{x}+\frac{73}{10}$ . Simplify the expression for $c(x)$ by performing the indicated addition.

Express the rational expression in lowest terms. - $\frac{y^{2}-3 y-18}{y^{2}+2 y-48}$

Suppose the triangles shown are similar, with angle $A=$ angle $D$ , angle $B=$ angle $E$ , and angle $C=$ angle $F$ . Answer the question. - What is the length of side DF?

Choose the one alternative that best completes the statement or answers the question. Determine whether the variation between the indicated quantities is direct or inverse. -The price of an item and the quantity of the item that you can purchase with a given amount of money

Write the rational expression in lowest terms. - $\frac{(y-3)(y-5)}{(5-y)(3+y)}$

Use two different methods to simplify the fraction. Explain each step of your work. $\frac{z-\frac{z+4}{24}}{\frac{5}{6}+\frac{7}{4 z}}$

Perform the indicated operation and express in lowest terms. - $\frac{2 p-2}{p} \div \frac{5 p-5}{7 p^{2}}$

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

Perform the indicated operation and express in lowest terms. - (2x−5)(x+2)(x+9)(x−3)÷(x+2)(3x+5)(x+9)(x−3)\frac{(2 x-5)(x+2)}{(x+9)(x-3)} \div \frac{(x+2)(3 x+5)}{(x+9)(x-3)}(x+9)(x−3)(2x−5)(x+2)​÷(x+9)(x−3)(x+2)(3x+5)​

Are the two expressions equivalent? If so, explain your answer. If not, choose values for xxx and ppp as a counter-example. 1x−1p\frac{1}{x}-\frac{1}{p}x1​−p1​ and 1x−p\frac{1}{x-p}x−p1​

Tell whether or not the rational expressions are equivalent. - 18x2y436x3y2,2y24x\frac{18 x^{2} y^{4}}{36 x^{3} y^{2}}, \frac{2 y^{2}}{4 x}36x3y218x2y4​,4x2y2​

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - f(x)=x+13x+4f(x)=\frac{x+1}{3 x+4}f(x)=3x+4x+1​

Solve the problem. Round your answer, as needed. -On a map of the United States, the distance between Phoenix and Reno is 2.4 inches. The two cities are actually 768 miles apart. On this same map, what would be the distance between two cities that are 1216 miles apart?

Tell whether or not the rational expressions are equivalent. - x2(x+1)x(x−1),x(x+1)x−1\frac{x^{2}(x+1)}{x(x-1)}, \frac{x(x+1)}{x-1}x(x−1)x2(x+1)​,x−1x(x+1)​

1−32x=741-\frac{3}{2 x}=\frac{7}{4}1−2x3​=47​

1w+11+13w−8=−413w2+25w−88\frac{1}{w+11}+\frac{1}{3 w-8}=\frac{-41}{3 w^{2}+25 w-88}w+111​+3w−81​=3w2+25w−88−41​

Choose the one alternative that best completes the statement or answers the question. Determine whether the variation between the indicated quantities is direct or inverse. -The time it takes to drive 100 miles and the speed at which you drive

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - f(x)=x−38f(x)=\frac{x-3}{8}f(x)=8x−3​

Perform the indicated operation and express in lowest terms. - 1619x−819x\frac{16}{19 x}-\frac{8}{19 x}19x16​−19x8​

One maid can clean the house three times faster than another. Working together they can clean the entire house in 3 hours. How long would it take the faster maid cleaning alone?

Express the rational expression in lowest terms. - y2−3y−18y2+2y−48\frac{y^{2}-3 y-18}{y^{2}+2 y-48}y2+2y−48y2−3y−18​

Suppose the triangles shown are similar, with angle A=A=A= angle DDD , angle B=B=B= angle EEE , and angle C=C=C= angle FFF . Answer the question. - What is the length of side DF?

Choose the one alternative that best completes the statement or answers the question. Determine whether the variation between the indicated quantities is direct or inverse. -The price of an item and the quantity of the item that you can purchase with a given amount of money

Write the rational expression in lowest terms. - (y−3)(y−5)(5−y)(3+y)\frac{(y-3)(y-5)}{(5-y)(3+y)}(5−y)(3+y)(y−3)(y−5)​

Use two different methods to simplify the fraction. Explain each step of your work. z−z+42456+74z\frac{z-\frac{z+4}{24}}{\frac{5}{6}+\frac{7}{4 z}}65​+4z7​z−24z+4​​

Perform the indicated operation and express in lowest terms. - 2p−2p÷5p−57p2\frac{2 p-2}{p} \div \frac{5 p-5}{7 p^{2}}p2p−2​÷7p25p−5​

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

Perform the indicated operation and express in lowest terms. - $\frac{(2 x-5)(x+2)}{(x+9)(x-3)} \div \frac{(x+2)(3 x+5)}{(x+9)(x-3)}$

Are the two expressions equivalent? If so, explain your answer. If not, choose values for $x$ and $p$ as a counter-example. $\frac{1}{x}-\frac{1}{p}$ and $\frac{1}{x-p}$

Tell whether or not the rational expressions are equivalent. - $\frac{18 x^{2} y^{4}}{36 x^{3} y^{2}}, \frac{2 y^{2}}{4 x}$

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - $f(x)=\frac{x+1}{3 x+4}$

Tell whether or not the rational expressions are equivalent. - $\frac{x^{2}(x+1)}{x(x-1)}, \frac{x(x+1)}{x-1}$

$1-\frac{3}{2 x}=\frac{7}{4}$

$\frac{1}{w+11}+\frac{1}{3 w-8}=\frac{-41}{3 w^{2}+25 w-88}$

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - $f(x)=\frac{x-3}{8}$

Perform the indicated operation and express in lowest terms. - $\frac{16}{19 x}-\frac{8}{19 x}$

Express the rational expression in lowest terms. - $\frac{y^{2}-3 y-18}{y^{2}+2 y-48}$

Suppose the triangles shown are similar, with angle $A=$ angle $D$ , angle $B=$ angle $E$ , and angle $C=$ angle $F$ . Answer the question. - What is the length of side DF?

Write the rational expression in lowest terms. - $\frac{(y-3)(y-5)}{(5-y)(3+y)}$

Use two different methods to simplify the fraction. Explain each step of your work. $\frac{z-\frac{z+4}{24}}{\frac{5}{6}+\frac{7}{4 z}}$

Perform the indicated operation and express in lowest terms. - $\frac{2 p-2}{p} \div \frac{5 p-5}{7 p^{2}}$