Question 1

Simplify the complex fraction.
-$\frac{1+\frac{4}{5}}{1+\frac{1}{15}}$

Accepted Answer

A)  $\frac{27}{16}$ 
B)  $\frac{27}{4}$ 
C)  $\frac{9}{16}$ 
D)  $\frac{5}{4}$ 
A)  $\frac{27}{16}$ 
B)  $\frac{27}{4}$ 
C)  $\frac{9}{16}$ 
D)  $\frac{5}{4}$

Question 2

$\frac{x^{2}+3 x-25}{x-8}+\frac{x^{2}+2 x-17}{8-x}$

Accepted Answer

A)  $\frac{1}{x-8}$ 
B)  $-\frac{1}{x-8}$ 
C)  1 
D)  - 1 
A)  $\frac{1}{x-8}$ 
B)  $-\frac{1}{x-8}$ 
C)  1 
D)  - 1

Question 3

$\frac{x+13}{2 x}-\frac{x-7}{9 x}$

Accepted Answer

A)  $\frac{7 x+131}{18}$ 
B)  $\frac{7 x+131}{2 x}$ 
C)  $\frac{7 x+131}{18 x}$ 
D)  $\frac{7 x+131}{x}$ 
A)  $\frac{7 x+131}{18}$ 
B)  $\frac{7 x+131}{2 x}$ 
C)  $\frac{7 x+131}{18 x}$ 
D)  $\frac{7 x+131}{x}$

Question 4

The effective spring constant keff for two springs (with spring constants of $\mathrm{k}_{1}$ amd $\mathrm{k}_{2}$ ) placed in series is given by the formula $\mathrm{k}_{\mathrm{eff}}=\frac{\mathrm{k}_{1} \mathrm{k}_{2}}{\mathrm{k}_{1}+\mathrm{k}_{2}}$. Solve the equation for $\mathrm{k}_{2}$.

Accepted Answer

A)  $\mathrm{k}_{2}=\frac{\mathrm{k}_{\mathrm{eff}} \mathrm{k}_{1}}{\mathrm{k}_{1}+\mathrm{k}_{\mathrm{eff}}}$ 
B)  $\mathrm{k}_{2}=\frac{\mathrm{k}_{\mathrm{eff}} \mathrm{k}_{1}}{\mathrm{k}_{1}-\mathrm{k}_{\mathrm{eff}}}$ 
C)  $\mathrm{k}_{2}=\frac{\mathrm{k}_{\mathrm{eff}}-\mathrm{k}_{1}}{\mathrm{k}_{1}}$ 
D)  $\mathrm{k}_{2}=\frac{\mathrm{k}_{\mathrm{eff}} \mathrm{k}_{1}}{\mathrm{k}_{\mathrm{eff}}-\mathrm{k}_{1}}$ 
A)  $\mathrm{k}_{2}=\frac{\mathrm{k}_{\mathrm{eff}} \mathrm{k}_{1}}{\mathrm{k}_{1}+\mathrm{k}_{\mathrm{eff}}}$ 
B)  $\mathrm{k}_{2}=\frac{\mathrm{k}_{\mathrm{eff}} \mathrm{k}_{1}}{\mathrm{k}_{1}-\mathrm{k}_{\mathrm{eff}}}$ 
C)  $\mathrm{k}_{2}=\frac{\mathrm{k}_{\mathrm{eff}}-\mathrm{k}_{1}}{\mathrm{k}_{1}}$ 
D)  $\mathrm{k}_{2}=\frac{\mathrm{k}_{\mathrm{eff}} \mathrm{k}_{1}}{\mathrm{k}_{\mathrm{eff}}-\mathrm{k}_{1}}$

Question 5

Find the LCD of the given rational expressions.
-$\frac{7}{x^{2}-7 x+10}, \frac{7}{x^{2}-8 x+12}$

Accepted Answer

A)  $(x-2)(x-6)$ 
B)  $(x-5)(x-2)(x-6)$ 
C)  $(x-5)(x-2)$ 
D)  $(x+5)(x+2)(x-6)$ 
A)  $(x-2)(x-6)$ 
B)  $(x-5)(x-2)(x-6)$ 
C)  $(x-5)(x-2)$ 
D)  $(x+5)(x+2)(x-6)$

Question 6

$\frac{7 x}{x^{2}-5 x+6}-\frac{28}{x^{2}-6 x+8}$

Accepted Answer

A)  $\frac{7}{(x-2)(x-3)}$ 
B)  $\frac{x-6}{(x-3)(x-4)}$ 
C)  $\frac{7 x-28}{(x-2)(x-3)(x-4)}$ 
D)  $\frac{7(x-6)}{(x-3)(x-4)}$ 
A)  $\frac{7}{(x-2)(x-3)}$ 
B)  $\frac{x-6}{(x-3)(x-4)}$ 
C)  $\frac{7 x-28}{(x-2)(x-3)(x-4)}$ 
D)  $\frac{7(x-6)}{(x-3)(x-4)}$

Question 7

Simplify the complex fraction.
-$\frac{\frac{x^{2}-5 x-14}{x^{2}-16 x+63}}{\frac{x^{2}+4 x-5}{x^{2}+2 x-3}}$

Accepted Answer

A)  $\frac{(\mathrm{x}+2)(\mathrm{x}-5)}{(\mathrm{x}-7)(\mathrm{x}+9)}$ 
B)  $\frac{\mathrm{x}-7}{\mathrm{x}-1}$ 
C)  $\frac{(x-2)(x+5)}{(x+7)(x-9)}$ 
D)  $\frac{(\mathrm{x}+2)(\mathrm{x}+3)}{(\mathrm{x}+5)(\mathrm{x}-9)}$ 
A)  $\frac{(\mathrm{x}+2)(\mathrm{x}-5)}{(\mathrm{x}-7)(\mathrm{x}+9)}$ 
B)  $\frac{\mathrm{x}-7}{\mathrm{x}-1}$ 
C)  $\frac{(x-2)(x+5)}{(x+7)(x-9)}$ 
D)  $\frac{(\mathrm{x}+2)(\mathrm{x}+3)}{(\mathrm{x}+5)(\mathrm{x}-9)}$

Question 8

Determine whether the two binomials are an opposites.
-$2 x-3$ and $3 x-2$

Accepted Answer

A) True 
 B)False

Question 9

Frank can type a report in 6 hours. James takes 8 hours to type it. How long will it take the two of them typing together?

Accepted Answer

A)  24 hours 
B)  $\frac{1}{14}$ hours 
C)  $3 \frac{3}{7}$ hours 
D)  $\frac{1}{48}$ hours 
A)  24 hours 
B)  $\frac{1}{14}$ hours 
C)  $3 \frac{3}{7}$ hours 
D)  $\frac{1}{48}$ hours

Question 10

$\frac{x+1}{x+6}-\frac{x}{x^{2}-36}=\frac{x-3}{x-6}$

Accepted Answer

A)  $\left\{\frac{5}{4}\right\}$ 
B)  $\left\{\frac{4}{3}\right\}$ 
C)  $\left\{\frac{4}{5}\right\}$ 
D)  $\left\{\frac{3}{4}\right\}$ 
A)  $\left\{\frac{5}{4}\right\}$ 
B)  $\left\{\frac{4}{3}\right\}$ 
C)  $\left\{\frac{4}{5}\right\}$ 
D)  $\left\{\frac{3}{4}\right\}$

Question 11

$\frac{4 \mathrm{x}-1}{\mathrm{x}^{2}+9 \mathrm{x}+8}-\frac{\mathrm{x}-2}{\mathrm{x}^{2}-1}$

Accepted Answer

A)  $\frac{3 x^{2}-11 x+17}{(x+1)(x-1)(x+8)}$ 
B)  $\frac{5 x^{2}+1 x-15}{(x+1)(x-1)(x+8)}$ 
C)  $\frac{5 x-3}{(x+1)(x+8)}$ 
D)  $\frac{3 \mathrm{x}+1}{(\mathrm{x}+1)(\mathrm{x}-1)}$ 
A)  $\frac{3 x^{2}-11 x+17}{(x+1)(x-1)(x+8)}$ 
B)  $\frac{5 x^{2}+1 x-15}{(x+1)(x-1)(x+8)}$ 
C)  $\frac{5 x-3}{(x+1)(x+8)}$ 
D)  $\frac{3 \mathrm{x}+1}{(\mathrm{x}+1)(\mathrm{x}-1)}$

Question 12

Find the LCD of the given rational expressions.
-$\frac{4}{6 x-48}, \frac{7}{x^{2}-8 x}$

Accepted Answer

A)  $6 x^{2}-48$ 
B)  $6 x^{2}-8$ 
C)  $6 x-8$ 
D)  $6 x(x-8)$ 
A)  $6 x^{2}-48$ 
B)  $6 x^{2}-8$ 
C)  $6 x-8$ 
D)  $6 x(x-8)$

Question 13

$\frac{2}{\mathrm{x}}=\frac{\mathrm{x}}{5 \mathrm{x}-12}$

Accepted Answer

A)  $\left\{0, \frac{8}{3}\right\}$ 
B)  $\{0\}$ 
C)  $\{4,6\}$ 
D)  $\{0,36\}$ 
A)  $\left\{0, \frac{8}{3}\right\}$ 
B)  $\{0\}$ 
C)  $\{4,6\}$ 
D)  $\{0,36\}$

Question 14

$y$ varies inversely as $x$. If $y=\frac{5}{2}$ when $x=5$, find $y$ when $x=6$.

Accepted Answer

A)  $\frac{1}{3}$ 
B)  $\frac{25}{12}$ 
C)  $\frac{5}{6}$ 
D)  3 
A)  $\frac{1}{3}$ 
B)  $\frac{25}{12}$ 
C)  $\frac{5}{6}$ 
D)  3

Question 15

$\frac{x^{2}-1}{3 x+3} \cdot \frac{x+3}{x-1}$

Accepted Answer

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

Question 16

One maid can clean the house in 4 hours. Another maid can do the job in 8 hours. How long will it take them to do the job working together?

Accepted Answer

A)  8 hours 
B)  $2 \frac{2}{3}$ hours 
C)  $\frac{1}{12}$ hours 
D)  $\frac{1}{32}$ hours 
A)  8 hours 
B)  $2 \frac{2}{3}$ hours 
C)  $\frac{1}{12}$ hours 
D)  $\frac{1}{32}$ hours

Question 17

Identify the given function as a linear function, a 
-$f(x)=\frac{4}{9} x+\frac{1}{3}$

Accepted Answer

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

Question 18

Evaluate the rational expression for the given value of the variable.
-$\frac{x-1}{4 x+6}$ for $x=-2$

Accepted Answer

A)  $\frac{3}{8}$ 
B)  $\frac{3}{20}$ 
C)  $-\frac{3}{5}$ 
D)  $\frac{3}{2}$ 
A)  $\frac{3}{8}$ 
B)  $\frac{3}{20}$ 
C)  $-\frac{3}{5}$ 
D)  $\frac{3}{2}$

Question 19

$\frac{4 x+8}{x-3} \cdot \frac{2 x^{2}-12 x+18}{x^{2}-4}$

Accepted Answer

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

Question 20

$\frac{6 \mathrm{x}}{7 \mathrm{x}-1}-\frac{18}{7 \mathrm{x}-1}$

Accepted Answer

A)  $\frac{6 x-18}{7 x-1}$ 
B)  $\frac{x-3}{7 x-1}$ 
C)  $\frac{6(x+3)}{7 x-1}$ 
D)  $\frac{6(x-3)}{7 x-1}$ 
A)  $\frac{6 x-18}{7 x-1}$ 
B)  $\frac{x-3}{7 x-1}$ 
C)  $\frac{6(x+3)}{7 x-1}$ 
D)  $\frac{6(x-3)}{7 x-1}$

Simplify the complex fraction. - $\frac{1+\frac{4}{5}}{1+\frac{1}{15}}$

$\frac{x^{2}+3 x-25}{x-8}+\frac{x^{2}+2 x-17}{8-x}$

$\frac{x+13}{2 x}-\frac{x-7}{9 x}$

The effective spring constant keff for two springs (with spring constants of $\mathrm{k}_{1}$ amd $\mathrm{k}_{2}$ ) placed in series is given by the formula $\mathrm{k}_{\mathrm{eff}}=\frac{\mathrm{k}_{1} \mathrm{k}_{2}}{\mathrm{k}_{1}+\mathrm{k}_{2}}$ . Solve the equation for $\mathrm{k}_{2}$ .

Find the LCD of the given rational expressions. - $\frac{7}{x^{2}-7 x+10}, \frac{7}{x^{2}-8 x+12}$

$\frac{7 x}{x^{2}-5 x+6}-\frac{28}{x^{2}-6 x+8}$

Simplify the complex fraction. - $\frac{\frac{x^{2}-5 x-14}{x^{2}-16 x+63}}{\frac{x^{2}+4 x-5}{x^{2}+2 x-3}}$

Determine whether the two binomials are an opposites. - $2 x-3$ and $3 x-2$

Frank can type a report in 6 hours. James takes 8 hours to type it. How long will it take the two of them typing together?

$\frac{x+1}{x+6}-\frac{x}{x^{2}-36}=\frac{x-3}{x-6}$

$\frac{4 \mathrm{x}-1}{\mathrm{x}^{2}+9 \mathrm{x}+8}-\frac{\mathrm{x}-2}{\mathrm{x}^{2}-1}$

Find the LCD of the given rational expressions. - $\frac{4}{6 x-48}, \frac{7}{x^{2}-8 x}$

$\frac{2}{\mathrm{x}}=\frac{\mathrm{x}}{5 \mathrm{x}-12}$

$y$ varies inversely as $x$ . If $y=\frac{5}{2}$ when $x=5$ , find $y$ when $x=6$ .

$\frac{x^{2}-1}{3 x+3} \cdot \frac{x+3}{x-1}$

One maid can clean the house in 4 hours. Another maid can do the job in 8 hours. How long will it take them to do the job working together?

Identify the given function as a linear function, a - $f(x)=\frac{4}{9} x+\frac{1}{3}$

Evaluate the rational expression for the given value of the variable. - $\frac{x-1}{4 x+6}$ for $x=-2$

$\frac{4 x+8}{x-3} \cdot \frac{2 x^{2}-12 x+18}{x^{2}-4}$

$\frac{6 \mathrm{x}}{7 \mathrm{x}-1}-\frac{18}{7 \mathrm{x}-1}$

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

Simplify the complex fraction. - 1+451+115\frac{1+\frac{4}{5}}{1+\frac{1}{15}}1+151​1+54​​

x2+3x−25x−8+x2+2x−178−x\frac{x^{2}+3 x-25}{x-8}+\frac{x^{2}+2 x-17}{8-x}x−8x2+3x−25​+8−xx2+2x−17​

x+132x−x−79x\frac{x+13}{2 x}-\frac{x-7}{9 x}2xx+13​−9xx−7​

Find the LCD of the given rational expressions. - 7x2−7x+10,7x2−8x+12\frac{7}{x^{2}-7 x+10}, \frac{7}{x^{2}-8 x+12}x2−7x+107​,x2−8x+127​

7xx2−5x+6−28x2−6x+8\frac{7 x}{x^{2}-5 x+6}-\frac{28}{x^{2}-6 x+8}x2−5x+67x​−x2−6x+828​

Simplify the complex fraction. - x2−5x−14x2−16x+63x2+4x−5x2+2x−3\frac{\frac{x^{2}-5 x-14}{x^{2}-16 x+63}}{\frac{x^{2}+4 x-5}{x^{2}+2 x-3}}x2+2x−3x2+4x−5​x2−16x+63x2−5x−14​​

Determine whether the two binomials are an opposites. - 2x−32 x-32x−3 and 3x−23 x-23x−2

Frank can type a report in 6 hours. James takes 8 hours to type it. How long will it take the two of them typing together?

x+1x+6−xx2−36=x−3x−6\frac{x+1}{x+6}-\frac{x}{x^{2}-36}=\frac{x-3}{x-6}x+6x+1​−x2−36x​=x−6x−3​

4x−1x2+9x+8−x−2x2−1\frac{4 \mathrm{x}-1}{\mathrm{x}^{2}+9 \mathrm{x}+8}-\frac{\mathrm{x}-2}{\mathrm{x}^{2}-1}x2+9x+84x−1​−x2−1x−2​

Find the LCD of the given rational expressions. - 46x−48,7x2−8x\frac{4}{6 x-48}, \frac{7}{x^{2}-8 x}6x−484​,x2−8x7​

2x=x5x−12\frac{2}{\mathrm{x}}=\frac{\mathrm{x}}{5 \mathrm{x}-12}x2​=5x−12x​

yyy varies inversely as xxx . If y=52y=\frac{5}{2}y=25​ when x=5x=5x=5 , find yyy when x=6x=6x=6 .

x2−13x+3⋅x+3x−1\frac{x^{2}-1}{3 x+3} \cdot \frac{x+3}{x-1}3x+3x2−1​⋅x−1x+3​

One maid can clean the house in 4 hours. Another maid can do the job in 8 hours. How long will it take them to do the job working together?

Identify the given function as a linear function, a - f(x)=49x+13f(x)=\frac{4}{9} x+\frac{1}{3}f(x)=94​x+31​

Evaluate the rational expression for the given value of the variable. - x−14x+6\frac{x-1}{4 x+6}4x+6x−1​ for x=−2x=-2x=−2

4x+8x−3⋅2x2−12x+18x2−4\frac{4 x+8}{x-3} \cdot \frac{2 x^{2}-12 x+18}{x^{2}-4}x−34x+8​⋅x2−42x2−12x+18​

6x7x−1−187x−1\frac{6 \mathrm{x}}{7 \mathrm{x}-1}-\frac{18}{7 \mathrm{x}-1}7x−16x​−7x−118​

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

Simplify the complex fraction. - $\frac{1+\frac{4}{5}}{1+\frac{1}{15}}$

$\frac{x^{2}+3 x-25}{x-8}+\frac{x^{2}+2 x-17}{8-x}$

$\frac{x+13}{2 x}-\frac{x-7}{9 x}$

Find the LCD of the given rational expressions. - $\frac{7}{x^{2}-7 x+10}, \frac{7}{x^{2}-8 x+12}$

$\frac{7 x}{x^{2}-5 x+6}-\frac{28}{x^{2}-6 x+8}$

Simplify the complex fraction. - $\frac{\frac{x^{2}-5 x-14}{x^{2}-16 x+63}}{\frac{x^{2}+4 x-5}{x^{2}+2 x-3}}$

Determine whether the two binomials are an opposites. - $2 x-3$ and $3 x-2$

$\frac{x+1}{x+6}-\frac{x}{x^{2}-36}=\frac{x-3}{x-6}$

$\frac{4 \mathrm{x}-1}{\mathrm{x}^{2}+9 \mathrm{x}+8}-\frac{\mathrm{x}-2}{\mathrm{x}^{2}-1}$

Find the LCD of the given rational expressions. - $\frac{4}{6 x-48}, \frac{7}{x^{2}-8 x}$

$\frac{2}{\mathrm{x}}=\frac{\mathrm{x}}{5 \mathrm{x}-12}$

$y$ varies inversely as $x$ . If $y=\frac{5}{2}$ when $x=5$ , find $y$ when $x=6$ .

$\frac{x^{2}-1}{3 x+3} \cdot \frac{x+3}{x-1}$

Identify the given function as a linear function, a - $f(x)=\frac{4}{9} x+\frac{1}{3}$

Evaluate the rational expression for the given value of the variable. - $\frac{x-1}{4 x+6}$ for $x=-2$

$\frac{4 x+8}{x-3} \cdot \frac{2 x^{2}-12 x+18}{x^{2}-4}$

$\frac{6 \mathrm{x}}{7 \mathrm{x}-1}-\frac{18}{7 \mathrm{x}-1}$