Question 1

$\frac{3}{10 \mathrm{x}}+\frac{9}{14 \mathrm{x}^{2}}$

Accepted Answer

A)  $\frac{12}{140 x^{2}}$ 
B)  $\frac{108}{70 x^{2}}$ 
C)  $\frac{21 x+45}{70 x^{2}}$ 
D)  $\frac{12}{10 x+14 x^{2}}$ 
A)  $\frac{12}{140 x^{2}}$ 
B)  $\frac{108}{70 x^{2}}$ 
C)  $\frac{21 x+45}{70 x^{2}}$ 
D)  $\frac{12}{10 x+14 x^{2}}$

Question 2

Identify the given function as a linear function, a 
-$f(x)=4 x+2$

Accepted Answer

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

Question 3

$\frac{8 x}{x^{2}-5 x+6}-\frac{32}{x^{2}-6 x+8}$

Accepted Answer

A)  $\frac{x-6}{(x-3)(x-4)}$ 
B)  $\frac{8 x-32}{(x-2)(x-3)(x-4)}$ 
C)  $\frac{8}{(x-2)(x-3)}$ 
D)  $\frac{8(x-6)}{(x-3)(x-4)}$ 
A)  $\frac{x-6}{(x-3)(x-4)}$ 
B)  $\frac{8 x-32}{(x-2)(x-3)(x-4)}$ 
C)  $\frac{8}{(x-2)(x-3)}$ 
D)  $\frac{8(x-6)}{(x-3)(x-4)}$

Question 4

$\frac{6 x-24}{16-x^{2}} \cdot \frac{5 x^{2}+6 x+1}{30 x+6}$

Accepted Answer

A)  $\frac{x+1}{x+4}$ 
B)  $-\frac{6(x+1)}{x+4}$ 
C)  $\frac{x+1}{4-x}$ 
D)  $-\frac{x+1}{x+4}$ 
A)  $\frac{x+1}{x+4}$ 
B)  $-\frac{6(x+1)}{x+4}$ 
C)  $\frac{x+1}{4-x}$ 
D)  $-\frac{x+1}{x+4}$

Question 5

$\frac{x}{x+4}+\frac{8 x+28}{x^{2}+7 x+12}=\frac{4}{x+3}$

Accepted Answer

A)  $\{3,-4\}$ 
B)  $\{6,5\}$ 
C)  $\{4,3\}$ 
D)  $\varnothing$ 
A)  $\{3,-4\}$ 
B)  $\{6,5\}$ 
C)  $\{4,3\}$ 
D)  $\varnothing$

Question 6

The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container $4 \mathrm{~cm}$ on a side is 192 grams, find the weight of the liquid in a cubical container $5 \mathrm{~cm}$ on a side.

Accepted Answer

A)  125 grams 
B)  105 grams 
C)  375 grams 
D)  15 grams 
A)  125 grams 
B)  105 grams 
C)  375 grams 
D)  15 grams

Question 7

Find any vertical asymptotes as well as the location of any holes in the graph of the given rational function.
-$f(x)=\frac{x^{2}-5 x-36}{x-9}$

Accepted Answer

A)  vertical asymptotes: none; hole: $(9,0)$ 
B)  vertical asymptotes: none; hole: $(9,13)$ 
C)  vertical asymptotes: $x=-4, x=9$; hole: $(-4,-13)$ 
D)  vertical asymptote: $x=9$; holes: none 
A)  vertical asymptotes: none; hole: $(9,0)$ 
B)  vertical asymptotes: none; hole: $(9,13)$ 
C)  vertical asymptotes: $x=-4, x=9$; hole: $(-4,-13)$ 
D)  vertical asymptote: $x=9$; holes: none

Question 8

For the given rational functions $f(x)$ and $g(x), f(x)+g(x)$.
-$f(x)=\frac{2 x+4}{3 x+7}, g(x)=\frac{4 x+10}{3 x+7}$

Accepted Answer

A)  $\frac{4 x+8}{3 x+7}$ 
B)  1 
C)  2 
D)  $\frac{2}{3 x+7}$ 
A)  $\frac{4 x+8}{3 x+7}$ 
B)  1 
C)  2 
D)  $\frac{2}{3 x+7}$

Question 9

$\frac{5}{x+6}+\frac{3}{x}$

Accepted Answer

A)  $\frac{8 x+18}{x(x+6)}$ 
B)  $\frac{5 x+18}{x(x+6)}$ 
C)  $\frac{8 x+18}{x}$ 
D)  $\frac{8 x+18}{(x+6)}$ 
A)  $\frac{8 x+18}{x(x+6)}$ 
B)  $\frac{5 x+18}{x(x+6)}$ 
C)  $\frac{8 x+18}{x}$ 
D)  $\frac{8 x+18}{(x+6)}$

Question 10

Solve for the specified variable
-$S=\frac{a}{1-r}$ for $r$

Accepted Answer

A)  $r=S-a$ 
B)  $r=\frac{a}{S}$ 
C)  $r=\frac{a}{S}-1$ 
D)  $r=\frac{S-a}{S}$ 
A)  $r=S-a$ 
B)  $r=\frac{a}{S}$ 
C)  $r=\frac{a}{S}-1$ 
D)  $r=\frac{S-a}{S}$

Question 11

For the given rational functions $f(x)$ and $g(x), f(x)$ - $g(x)$.
-$f(x)=\frac{3 x^{2}+8}{x^{2}+7 x-8}, g(x)=\frac{10 x}{x^{2}+7 x-8}$

Accepted Answer

A)  $\frac{(x-2)(3 x-4)}{(x+8)(x-1)}$ 
B)  $\frac{(\mathrm{x}-2)(3 \mathrm{x}+4)}{(\mathrm{x}+8)(\mathrm{x}-1)}$ 
C)  $\frac{3 x-4}{x-1}$ 
D)  $\frac{(x+2)(3 x+4)}{(x+8)(x-1)}$ 
A)  $\frac{(x-2)(3 x-4)}{(x+8)(x-1)}$ 
B)  $\frac{(\mathrm{x}-2)(3 \mathrm{x}+4)}{(\mathrm{x}+8)(\mathrm{x}-1)}$ 
C)  $\frac{3 x-4}{x-1}$ 
D)  $\frac{(x+2)(3 x+4)}{(x+8)(x-1)}$

Question 12

$\frac{\mathrm{x}^{2}-7}{\mathrm{x}-4}=\frac{9}{\mathrm{x}-4}$

Accepted Answer

A)  $\{-4\}$ 
B)  $\{4\}$. 
C)  $\{-4,4\}$ 
D)  $\varnothing$ 
A)  $\{-4\}$ 
B)  $\{4\}$. 
C)  $\{-4,4\}$ 
D)  $\varnothing$

Question 13

Find all values of the variable for which the rational expression is undefined.
-$\frac{x-6}{6 x-24}$

Accepted Answer

A)  0 
B)  4 
C)  24 
D)  -6 
A)  0 
B)  4 
C)  24 
D)  -6

Question 14

Solve for the specified variable
-$I=\frac{k E}{R}$ for $R$

Accepted Answer

A)  $\mathrm{R}=\mathrm{kEI}$ 
B)  $\mathrm{R}=\mathrm{kE}-\mathrm{I}$ 
C)  $R=\frac{k E}{I}$ 
D)  $\mathrm{R}=\frac{\mathrm{I}}{\mathrm{kE}}$ 
A)  $\mathrm{R}=\mathrm{kEI}$ 
B)  $\mathrm{R}=\mathrm{kE}-\mathrm{I}$ 
C)  $R=\frac{k E}{I}$ 
D)  $\mathrm{R}=\frac{\mathrm{I}}{\mathrm{kE}}$

Question 15

Find $r(0)$.

Accepted Answer

A)  2 
B)  1 
C)  0 
D)  -2 
A)  2 
B)  1 
C)  0 
D)  -2

Question 16

$\frac{1}{2-\mathrm{x}}=\frac{1-\mathrm{x}}{\mathrm{x}-2}$

Accepted Answer

A)   $\{2\}$ 
B)  $\{0\}$ 
C)  $\{1\}$ 
D)  $\varnothing$ 
A)   $\{2\}$ 
B)  $\{0\}$ 
C)  $\{1\}$ 
D)  $\varnothing$

Question 17

For the given rational functions $f(x)$ and $g(x), f(x)$ - $g(x)$.
-$f(x)=\frac{2 x+8}{x^{2}+5 x+4}, g(x)=\frac{x+4}{x^{2}+5 x+4}$

Accepted Answer

A)  $\frac{x+12}{x^{2}+5 x+4}$ 
B)  $\frac{1}{\mathrm{x}+1}$ 
C)  $x+4$ 
D)  $\frac{9}{x^{2}+5 x+4}$ 
A)  $\frac{x+12}{x^{2}+5 x+4}$ 
B)  $\frac{1}{\mathrm{x}+1}$ 
C)  $x+4$ 
D)  $\frac{9}{x^{2}+5 x+4}$

Question 18

For the given rational functions $f(x)$ and $g(x), f(x)+g(x)$.
-$f(x)=\frac{6}{x}, g(x)=\frac{13}{x}$

Accepted Answer

A)  $\frac{19}{\mathrm{x}}$ 
B)  $\frac{78}{x}$ 
C)  $\frac{x+19}{x}$ 
D)  $19 x$ 
A)  $\frac{19}{\mathrm{x}}$ 
B)  $\frac{78}{x}$ 
C)  $\frac{x+19}{x}$ 
D)  $19 x$

Question 19

$\frac{3}{\mathrm{x}^{2}-11 \mathrm{x}+30}-\frac{1}{\mathrm{x}-6}=\frac{1}{9 \mathrm{x}-45}$

Accepted Answer

A)  $\left\{-\frac{4}{3}\right\}$ 
B)  $\left\{\frac{39}{5}\right\}$ 
C)  $\{6\}$ 
D)  $\left\{\frac{27}{5}\right\}$ 
A)  $\left\{-\frac{4}{3}\right\}$ 
B)  $\left\{\frac{39}{5}\right\}$ 
C)  $\{6\}$ 
D)  $\left\{\frac{27}{5}\right\}$

Question 20

Determine whether the two binomials are an opposites.
-8 - $x$ and $x-8$

Accepted Answer

A) True 
 B)False

$\frac{3}{10 \mathrm{x}}+\frac{9}{14 \mathrm{x}^{2}}$

Identify the given function as a linear function, a - $f(x)=4 x+2$

$\frac{8 x}{x^{2}-5 x+6}-\frac{32}{x^{2}-6 x+8}$

$\frac{6 x-24}{16-x^{2}} \cdot \frac{5 x^{2}+6 x+1}{30 x+6}$

$\frac{x}{x+4}+\frac{8 x+28}{x^{2}+7 x+12}=\frac{4}{x+3}$

The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container $4 \mathrm{~cm}$ on a side is 192 grams, find the weight of the liquid in a cubical container $5 \mathrm{~cm}$ on a side.

Find any vertical asymptotes as well as the location of any holes in the graph of the given rational function. - $f(x)=\frac{x^{2}-5 x-36}{x-9}$

For the given rational functions $f(x)$ and $g(x), f(x)+g(x)$ . - $f(x)=\frac{2 x+4}{3 x+7}, g(x)=\frac{4 x+10}{3 x+7}$

$\frac{5}{x+6}+\frac{3}{x}$

Solve for the specified variable - $S=\frac{a}{1-r}$ for $r$

For the given rational functions $f(x)$ and $g(x), f(x)$ - $g(x)$ . - $f(x)=\frac{3 x^{2}+8}{x^{2}+7 x-8}, g(x)=\frac{10 x}{x^{2}+7 x-8}$

$\frac{\mathrm{x}^{2}-7}{\mathrm{x}-4}=\frac{9}{\mathrm{x}-4}$

Find all values of the variable for which the rational expression is undefined. - $\frac{x-6}{6 x-24}$

Solve for the specified variable - $I=\frac{k E}{R}$ for $R$

Find $r(0)$ .

$\frac{1}{2-\mathrm{x}}=\frac{1-\mathrm{x}}{\mathrm{x}-2}$

For the given rational functions $f(x)$ and $g(x), f(x)$ - $g(x)$ . - $f(x)=\frac{2 x+8}{x^{2}+5 x+4}, g(x)=\frac{x+4}{x^{2}+5 x+4}$

For the given rational functions $f(x)$ and $g(x), f(x)+g(x)$ . - $f(x)=\frac{6}{x}, g(x)=\frac{13}{x}$

$\frac{3}{\mathrm{x}^{2}-11 \mathrm{x}+30}-\frac{1}{\mathrm{x}-6}=\frac{1}{9 \mathrm{x}-45}$

Determine whether the two binomials are an opposites. -8 - $x$ and $x-8$

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

310x+914x2\frac{3}{10 \mathrm{x}}+\frac{9}{14 \mathrm{x}^{2}}10x3​+14x29​

Identify the given function as a linear function, a - f(x)=4x+2f(x)=4 x+2f(x)=4x+2

8xx2−5x+6−32x2−6x+8\frac{8 x}{x^{2}-5 x+6}-\frac{32}{x^{2}-6 x+8}x2−5x+68x​−x2−6x+832​

6x−2416−x2⋅5x2+6x+130x+6\frac{6 x-24}{16-x^{2}} \cdot \frac{5 x^{2}+6 x+1}{30 x+6}16−x26x−24​⋅30x+65x2+6x+1​

xx+4+8x+28x2+7x+12=4x+3\frac{x}{x+4}+\frac{8 x+28}{x^{2}+7 x+12}=\frac{4}{x+3}x+4x​+x2+7x+128x+28​=x+34​

The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 4 cm4 \mathrm{~cm}4 cm on a side is 192 grams, find the weight of the liquid in a cubical container 5 cm5 \mathrm{~cm}5 cm on a side.

Find any vertical asymptotes as well as the location of any holes in the graph of the given rational function. - f(x)=x2−5x−36x−9f(x)=\frac{x^{2}-5 x-36}{x-9}f(x)=x−9x2−5x−36​

For the given rational functions f(x)f(x)f(x) and g(x),f(x)+g(x)g(x), f(x)+g(x)g(x),f(x)+g(x) . - f(x)=2x+43x+7,g(x)=4x+103x+7f(x)=\frac{2 x+4}{3 x+7}, g(x)=\frac{4 x+10}{3 x+7}f(x)=3x+72x+4​,g(x)=3x+74x+10​

5x+6+3x\frac{5}{x+6}+\frac{3}{x}x+65​+x3​

Solve for the specified variable - S=a1−rS=\frac{a}{1-r}S=1−ra​ for rrr

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)=3x2+8x2+7x−8,g(x)=10xx2+7x−8f(x)=\frac{3 x^{2}+8}{x^{2}+7 x-8}, g(x)=\frac{10 x}{x^{2}+7 x-8}f(x)=x2+7x−83x2+8​,g(x)=x2+7x−810x​

x2−7x−4=9x−4\frac{\mathrm{x}^{2}-7}{\mathrm{x}-4}=\frac{9}{\mathrm{x}-4}x−4x2−7​=x−49​

Find all values of the variable for which the rational expression is undefined. - x−66x−24\frac{x-6}{6 x-24}6x−24x−6​

Solve for the specified variable - I=kERI=\frac{k E}{R}I=RkE​ for RRR

Find r(0)r(0)r(0) .

12−x=1−xx−2\frac{1}{2-\mathrm{x}}=\frac{1-\mathrm{x}}{\mathrm{x}-2}2−x1​=x−21−x​

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)=2x+8x2+5x+4,g(x)=x+4x2+5x+4f(x)=\frac{2 x+8}{x^{2}+5 x+4}, g(x)=\frac{x+4}{x^{2}+5 x+4}f(x)=x2+5x+42x+8​,g(x)=x2+5x+4x+4​

For the given rational functions f(x)f(x)f(x) and g(x),f(x)+g(x)g(x), f(x)+g(x)g(x),f(x)+g(x) . - f(x)=6x,g(x)=13xf(x)=\frac{6}{x}, g(x)=\frac{13}{x}f(x)=x6​,g(x)=x13​

3x2−11x+30−1x−6=19x−45\frac{3}{\mathrm{x}^{2}-11 \mathrm{x}+30}-\frac{1}{\mathrm{x}-6}=\frac{1}{9 \mathrm{x}-45}x2−11x+303​−x−61​=9x−451​

Determine whether the two binomials are an opposites. -8 - xxx and x−8x-8x−8

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

$\frac{3}{10 \mathrm{x}}+\frac{9}{14 \mathrm{x}^{2}}$

Identify the given function as a linear function, a - $f(x)=4 x+2$

$\frac{8 x}{x^{2}-5 x+6}-\frac{32}{x^{2}-6 x+8}$

$\frac{6 x-24}{16-x^{2}} \cdot \frac{5 x^{2}+6 x+1}{30 x+6}$

$\frac{x}{x+4}+\frac{8 x+28}{x^{2}+7 x+12}=\frac{4}{x+3}$

The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container $4 \mathrm{~cm}$ on a side is 192 grams, find the weight of the liquid in a cubical container $5 \mathrm{~cm}$ on a side.

Find any vertical asymptotes as well as the location of any holes in the graph of the given rational function. - $f(x)=\frac{x^{2}-5 x-36}{x-9}$

For the given rational functions $f(x)$ and $g(x), f(x)+g(x)$ . - $f(x)=\frac{2 x+4}{3 x+7}, g(x)=\frac{4 x+10}{3 x+7}$

$\frac{5}{x+6}+\frac{3}{x}$

Solve for the specified variable - $S=\frac{a}{1-r}$ for $r$

For the given rational functions $f(x)$ and $g(x), f(x)$ - $g(x)$ . - $f(x)=\frac{3 x^{2}+8}{x^{2}+7 x-8}, g(x)=\frac{10 x}{x^{2}+7 x-8}$

$\frac{\mathrm{x}^{2}-7}{\mathrm{x}-4}=\frac{9}{\mathrm{x}-4}$

Find all values of the variable for which the rational expression is undefined. - $\frac{x-6}{6 x-24}$

Solve for the specified variable - $I=\frac{k E}{R}$ for $R$

Find $r(0)$ .

$\frac{1}{2-\mathrm{x}}=\frac{1-\mathrm{x}}{\mathrm{x}-2}$

For the given rational functions $f(x)$ and $g(x), f(x)$ - $g(x)$ . - $f(x)=\frac{2 x+8}{x^{2}+5 x+4}, g(x)=\frac{x+4}{x^{2}+5 x+4}$

For the given rational functions $f(x)$ and $g(x), f(x)+g(x)$ . - $f(x)=\frac{6}{x}, g(x)=\frac{13}{x}$

$\frac{3}{\mathrm{x}^{2}-11 \mathrm{x}+30}-\frac{1}{\mathrm{x}-6}=\frac{1}{9 \mathrm{x}-45}$

Determine whether the two binomials are an opposites. -8 - $x$ and $x-8$