Question 1

$\frac{5 x-20}{x^{2}-16}-\frac{5 x-20}{16-x^{2}}$

Accepted Answer

A)  $\frac{10}{x+4}$ 
B)  $\frac{10}{x-4}$ 
C)  0 
D)  10 
A)  $\frac{10}{x+4}$ 
B)  $\frac{10}{x-4}$ 
C)  0 
D)  10

Question 2

Find all values of the variable for which the rational expression is undefined.
-$\frac{x-4}{7-x}$

Accepted Answer

A)  7,4 
B)  None 
C)  7 
D)  -7 
A)  7,4 
B)  None 
C)  7 
D)  -7

Question 3

The speed of a vehicle varies inversely as the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 10 miles per hour in 60 minutes, how fast must it travel to cover the same distance in 20 minutes?

Accepted Answer

A)  $30 \mathrm{mph}$ 
B)  $\frac{3}{10} \mathrm{mph}$ 
C)  $120 \mathrm{mph}$ 
D)  $\frac{10}{3} \mathrm{mph}$ 
A)  $30 \mathrm{mph}$ 
B)  $\frac{3}{10} \mathrm{mph}$ 
C)  $120 \mathrm{mph}$ 
D)  $\frac{10}{3} \mathrm{mph}$

Question 4

$\frac{(\mathrm{x}-2)(\mathrm{x}+3)}{(\mathrm{x}+7)(\mathrm{x}-2)} \cdot \frac{(\mathrm{x}-10)(\mathrm{x}+7)}{(\mathrm{x}+3)(\mathrm{x}+6)}$

Accepted Answer

A)  $\frac{x-10}{x+6}$ 
B)  $-\frac{x-10}{x+6}$ 
C)  $\frac{x+3}{x-2}$ 
D)  $\frac{x+10}{x-6}$ 
A)  $\frac{x-10}{x+6}$ 
B)  $-\frac{x-10}{x+6}$ 
C)  $\frac{x+3}{x-2}$ 
D)  $\frac{x+10}{x-6}$

Question 5

Find all values $x$ such that $r(x)=0$.

Accepted Answer

A)  -5 
B)  5 
C)  -3 
D)  3 
A)  -5 
B)  5 
C)  -3 
D)  3

Question 6

$\frac{6}{\mathrm{x}}+\frac{7}{8}=1$

Accepted Answer

A)  $\{13\}$ 
B)  $\left\{\frac{13}{8}\right\}$ 
C)  $\{8\}$ 
D)  $\{48\}$ 
A)  $\{13\}$ 
B)  $\left\{\frac{13}{8}\right\}$ 
C)  $\{8\}$ 
D)  $\{48\}$

Question 7

For the given rational functions $f(x)$ and $g(x), f(x)$ - $g(x)$.
-$f(x)=\frac{9 x-2}{x^{2}+5 x-14}, g(x)=\frac{x+4}{x^{2}-4}$

Accepted Answer

A)  $\frac{10 x+2}{(x-2)(x+7)}$ 
B)  $\frac{8 \mathrm{x}-6}{(\mathrm{x}-2)(\mathrm{x}+2)}$ 
C)  $\frac{8 x^{2}+5 x-32}{(x-2)(x+2)(x+7)}$ 
D)  $\frac{10 x^{2}+27 x+24}{(x-2)(x+2)(x+7)}$ 
A)  $\frac{10 x+2}{(x-2)(x+7)}$ 
B)  $\frac{8 \mathrm{x}-6}{(\mathrm{x}-2)(\mathrm{x}+2)}$ 
C)  $\frac{8 x^{2}+5 x-32}{(x-2)(x+2)(x+7)}$ 
D)  $\frac{10 x^{2}+27 x+24}{(x-2)(x+2)(x+7)}$

Question 8

Simplify the complex fraction.
-$\frac{9+\frac{3}{x}}{\frac{x}{4}+\frac{1}{12}}$

Accepted Answer

A)  $\frac{x}{36}$ 
B)  36 
C)  1 
D)  $\frac{36}{x}$ 
A)  $\frac{x}{36}$ 
B)  36 
C)  1 
D)  $\frac{36}{x}$

Question 9

$\frac{x-4}{x-8}=\frac{4}{x-8}$

Accepted Answer

A)  $\{8\}$ 
B)  $\{-8\}$. 
C)  $\{0\}$ 
D)  $\varnothing$ 
A)  $\{8\}$ 
B)  $\{-8\}$. 
C)  $\{0\}$ 
D)  $\varnothing$

Question 10

$\frac{x^{2}-9 x}{x-7}+\frac{2 x-28}{7-x}$

Accepted Answer

A)  $x+4$ 
B)  $\frac{x^{2}-7 x-28}{x-7}$ 
C)  $-\frac{x^{2}-7 x-28}{x-7}$ 
D)  $x-4$ 
A)  $x+4$ 
B)  $\frac{x^{2}-7 x-28}{x-7}$ 
C)  $-\frac{x^{2}-7 x-28}{x-7}$ 
D)  $x-4$

Question 11

Solve for the specified variable
-$A=\frac{h(B+b)}{2}$ for $b$

Accepted Answer

A)  $b=2 A-B h$ 
B)  $b=\frac{2 A+B h}{h}$ 
C)  $b=\frac{2 A-B h}{h}$ 
D)  $b=\frac{A-B h}{h}$ 
A)  $b=2 A-B h$ 
B)  $b=\frac{2 A+B h}{h}$ 
C)  $b=\frac{2 A-B h}{h}$ 
D)  $b=\frac{A-B h}{h}$

Question 12

$\frac{6 x+2}{x^{2}+9 x}+\frac{x^{2}+8 x+43}{x^{2}+9 x}$

Accepted Answer

A)  $\frac{x-5}{x}$ 
B)  $x-5$ 
C)  $\frac{x+5}{x}$ 
D)  $\frac{x^{2}+14 x+45}{x^{2}+9 x}$ 
A)  $\frac{x-5}{x}$ 
B)  $x-5$ 
C)  $\frac{x+5}{x}$ 
D)  $\frac{x^{2}+14 x+45}{x^{2}+9 x}$

Question 13

$\frac{7 \mathrm{x}-12}{\mathrm{x}^{2}-4}-\frac{4 \mathrm{x}-6}{\mathrm{x}^{2}-4}$

Accepted Answer

A)  $-\frac{3}{x-2}$ 
B)  $\frac{3(x-2)}{x^{2}-4}$ 
C)  $\frac{3}{x-2}$ 
D)  $\frac{3}{x+2}$ 
A)  $-\frac{3}{x-2}$ 
B)  $\frac{3(x-2)}{x^{2}-4}$ 
C)  $\frac{3}{x-2}$ 
D)  $\frac{3}{x+2}$

Question 14

$\frac{x^{2}+9 x+18}{x+6} \div \frac{x^{2}-9}{6 x-18}$

Accepted Answer

A)  $\frac{6 x-18}{x-3}$ 
B)  $\frac{(x+3)^{2}}{6}$ 
C)  6 
D)  $\frac{1}{6}$ 
A)  $\frac{6 x-18}{x-3}$ 
B)  $\frac{(x+3)^{2}}{6}$ 
C)  6 
D)  $\frac{1}{6}$

Question 15

The number of patients Dr. Wong can see varies directly as the time it takes her to see them. If she can see 9 patients in 2 hours, how long would it take her to see 90 patients?

Accepted Answer

A)  405 hours 
B)  18 hours 
C)  19 hours 
D)  20 hours 
A)  405 hours 
B)  18 hours 
C)  19 hours 
D)  20 hours

Question 16

Find the missing numerator and denominator.
-$\frac{x^{2}+18 x+81}{x^{2}-16} \cdot \frac{?}{?}=\frac{x+9}{x+4}$

Accepted Answer

A)  $\frac{x+9}{x-4}$ 
B)  $\frac{x-9}{x+4}$ 
C)  $\frac{x-4}{x+9}$ 
D)  $\frac{x+9}{(x+4)^{2}}$ 
A)  $\frac{x+9}{x-4}$ 
B)  $\frac{x-9}{x+4}$ 
C)  $\frac{x-4}{x+9}$ 
D)  $\frac{x+9}{(x+4)^{2}}$

Question 17

Solve for the specified variable
-$P=\frac{A}{1+r t}$ for $r$

Accepted Answer

A)  $r=\frac{P-A}{1+t}$ 
B)  $r=\frac{P-1}{A t}$ 
C)  $r=\frac{A-P}{P t}$ 
D)  $r=P-t A$ 
A)  $r=\frac{P-A}{1+t}$ 
B)  $r=\frac{P-1}{A t}$ 
C)  $r=\frac{A-P}{P t}$ 
D)  $r=P-t A$

Question 18

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

Accepted Answer

A)  $\{-1\}$ 
B)  $\left\{\frac{15}{13}\right\}$ 
C)  $\left\{\frac{11}{13}\right\}$ 
D)  $\varnothing$ 
A)  $\{-1\}$ 
B)  $\left\{\frac{15}{13}\right\}$ 
C)  $\left\{\frac{11}{13}\right\}$ 
D)  $\varnothing$

Question 19

The intensity of a radio signal from a radio station varies inversely as the square of the distance from the station. If the intensity is 8000 units at a distance of 2 miles, what will it be at a distance of 13 miles?

Accepted Answer

A)  189 units 
B)  172 units 
C)  215 units 
D)  153 units 
A)  189 units 
B)  172 units 
C)  215 units 
D)  153 units

Question 20

Identify the given function as a linear function, a 
-$f(x)=\frac{1}{3} x^{2}-25$

Accepted Answer

A)  Linear 
B)  Quadratic 
C)  Rational 
A)  Linear 
B)  Quadratic 
C)  Rational

$\frac{5 x-20}{x^{2}-16}-\frac{5 x-20}{16-x^{2}}$

Find all values of the variable for which the rational expression is undefined. - $\frac{x-4}{7-x}$

The speed of a vehicle varies inversely as the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 10 miles per hour in 60 minutes, how fast must it travel to cover the same distance in 20 minutes?

$\frac{(\mathrm{x}-2)(\mathrm{x}+3)}{(\mathrm{x}+7)(\mathrm{x}-2)} \cdot \frac{(\mathrm{x}-10)(\mathrm{x}+7)}{(\mathrm{x}+3)(\mathrm{x}+6)}$

Find all values $x$ such that $r(x)=0$ .

$\frac{6}{\mathrm{x}}+\frac{7}{8}=1$

For the given rational functions $f(x)$ and $g(x), f(x)$ - $g(x)$ . - $f(x)=\frac{9 x-2}{x^{2}+5 x-14}, g(x)=\frac{x+4}{x^{2}-4}$

Simplify the complex fraction. - $\frac{9+\frac{3}{x}}{\frac{x}{4}+\frac{1}{12}}$

$\frac{x-4}{x-8}=\frac{4}{x-8}$

$\frac{x^{2}-9 x}{x-7}+\frac{2 x-28}{7-x}$

Solve for the specified variable - $A=\frac{h(B+b)}{2}$ for $b$

$\frac{6 x+2}{x^{2}+9 x}+\frac{x^{2}+8 x+43}{x^{2}+9 x}$

$\frac{7 \mathrm{x}-12}{\mathrm{x}^{2}-4}-\frac{4 \mathrm{x}-6}{\mathrm{x}^{2}-4}$

$\frac{x^{2}+9 x+18}{x+6} \div \frac{x^{2}-9}{6 x-18}$

The number of patients Dr. Wong can see varies directly as the time it takes her to see them. If she can see 9 patients in 2 hours, how long would it take her to see 90 patients?

Find the missing numerator and denominator. - $\frac{x^{2}+18 x+81}{x^{2}-16} \cdot \frac{?}{?}=\frac{x+9}{x+4}$

Solve for the specified variable - $P=\frac{A}{1+r t}$ for $r$

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

The intensity of a radio signal from a radio station varies inversely as the square of the distance from the station. If the intensity is 8000 units at a distance of 2 miles, what will it be at a distance of 13 miles?

Identify the given function as a linear function, a - $f(x)=\frac{1}{3} x^{2}-25$

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 6: Rational Expressions and Equations

5x−20x2−16−5x−2016−x2\frac{5 x-20}{x^{2}-16}-\frac{5 x-20}{16-x^{2}}x2−165x−20​−16−x25x−20​

Find all values of the variable for which the rational expression is undefined. - x−47−x\frac{x-4}{7-x}7−xx−4​

The speed of a vehicle varies inversely as the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 10 miles per hour in 60 minutes, how fast must it travel to cover the same distance in 20 minutes?

(x−2)(x+3)(x+7)(x−2)⋅(x−10)(x+7)(x+3)(x+6)\frac{(\mathrm{x}-2)(\mathrm{x}+3)}{(\mathrm{x}+7)(\mathrm{x}-2)} \cdot \frac{(\mathrm{x}-10)(\mathrm{x}+7)}{(\mathrm{x}+3)(\mathrm{x}+6)}(x+7)(x−2)(x−2)(x+3)​⋅(x+3)(x+6)(x−10)(x+7)​

Find all values xxx such that r(x)=0r(x)=0r(x)=0 .

6x+78=1\frac{6}{\mathrm{x}}+\frac{7}{8}=1x6​+87​=1

For the given rational functions f(x)f(x)f(x) and g(x),f(x)g(x), f(x)g(x),f(x) - g(x)g(x)g(x) . - f(x)=9x−2x2+5x−14,g(x)=x+4x2−4f(x)=\frac{9 x-2}{x^{2}+5 x-14}, g(x)=\frac{x+4}{x^{2}-4}f(x)=x2+5x−149x−2​,g(x)=x2−4x+4​

Simplify the complex fraction. - 9+3xx4+112\frac{9+\frac{3}{x}}{\frac{x}{4}+\frac{1}{12}}4x​+121​9+x3​​

x−4x−8=4x−8\frac{x-4}{x-8}=\frac{4}{x-8}x−8x−4​=x−84​

x2−9xx−7+2x−287−x\frac{x^{2}-9 x}{x-7}+\frac{2 x-28}{7-x}x−7x2−9x​+7−x2x−28​

Solve for the specified variable - A=h(B+b)2A=\frac{h(B+b)}{2}A=2h(B+b)​ for bbb

6x+2x2+9x+x2+8x+43x2+9x\frac{6 x+2}{x^{2}+9 x}+\frac{x^{2}+8 x+43}{x^{2}+9 x}x2+9x6x+2​+x2+9xx2+8x+43​

7x−12x2−4−4x−6x2−4\frac{7 \mathrm{x}-12}{\mathrm{x}^{2}-4}-\frac{4 \mathrm{x}-6}{\mathrm{x}^{2}-4}x2−47x−12​−x2−44x−6​

x2+9x+18x+6÷x2−96x−18\frac{x^{2}+9 x+18}{x+6} \div \frac{x^{2}-9}{6 x-18}x+6x2+9x+18​÷6x−18x2−9​

The number of patients Dr. Wong can see varies directly as the time it takes her to see them. If she can see 9 patients in 2 hours, how long would it take her to see 90 patients?

Find the missing numerator and denominator. - x2+18x+81x2−16⋅??=x+9x+4\frac{x^{2}+18 x+81}{x^{2}-16} \cdot \frac{?}{?}=\frac{x+9}{x+4}x2−16x2+18x+81​⋅??​=x+4x+9​

Solve for the specified variable - P=A1+rtP=\frac{A}{1+r t}P=1+rtA​ for rrr

4x−32x+1=2x−1x+4\frac{4 \mathrm{x}-3}{2 \mathrm{x}+1}=\frac{2 \mathrm{x}-1}{\mathrm{x}+4}2x+14x−3​=x+42x−1​

The intensity of a radio signal from a radio station varies inversely as the square of the distance from the station. If the intensity is 8000 units at a distance of 2 miles, what will it be at a distance of 13 miles?

Identify the given function as a linear function, a - f(x)=13x2−25f(x)=\frac{1}{3} x^{2}-25f(x)=31​x2−25

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

$\frac{5 x-20}{x^{2}-16}-\frac{5 x-20}{16-x^{2}}$

Find all values of the variable for which the rational expression is undefined. - $\frac{x-4}{7-x}$

$\frac{(\mathrm{x}-2)(\mathrm{x}+3)}{(\mathrm{x}+7)(\mathrm{x}-2)} \cdot \frac{(\mathrm{x}-10)(\mathrm{x}+7)}{(\mathrm{x}+3)(\mathrm{x}+6)}$

Find all values $x$ such that $r(x)=0$ .

$\frac{6}{\mathrm{x}}+\frac{7}{8}=1$

For the given rational functions $f(x)$ and $g(x), f(x)$ - $g(x)$ . - $f(x)=\frac{9 x-2}{x^{2}+5 x-14}, g(x)=\frac{x+4}{x^{2}-4}$

Simplify the complex fraction. - $\frac{9+\frac{3}{x}}{\frac{x}{4}+\frac{1}{12}}$

$\frac{x-4}{x-8}=\frac{4}{x-8}$

$\frac{x^{2}-9 x}{x-7}+\frac{2 x-28}{7-x}$

Solve for the specified variable - $A=\frac{h(B+b)}{2}$ for $b$

$\frac{6 x+2}{x^{2}+9 x}+\frac{x^{2}+8 x+43}{x^{2}+9 x}$

$\frac{7 \mathrm{x}-12}{\mathrm{x}^{2}-4}-\frac{4 \mathrm{x}-6}{\mathrm{x}^{2}-4}$

$\frac{x^{2}+9 x+18}{x+6} \div \frac{x^{2}-9}{6 x-18}$

Find the missing numerator and denominator. - $\frac{x^{2}+18 x+81}{x^{2}-16} \cdot \frac{?}{?}=\frac{x+9}{x+4}$

Solve for the specified variable - $P=\frac{A}{1+r t}$ for $r$

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

Identify the given function as a linear function, a - $f(x)=\frac{1}{3} x^{2}-25$