Question 1

Reduce the rational expression to lowest terms.   $\frac{r^2-81}{r^2-11r+18}$

Accepted Answer

$\frac{r+9}{r-2}$

Question 2

State the excluded values for the rational expression $\frac{r^2-81}{r^2-11r+18}$  {Note:  If there is more than one excluded value use the word "and" between each excluded value.}

Accepted Answer

2 and 9

Question 3

Reduce the rational expression to lowest terms.  $\frac{3(x+9)(x-7)}{21x-147}$

Accepted Answer

$\frac{x+9}{7}$

Question 4

What are the excluded values for the rational expression $\frac{3(x+9)(x-7)}{21x-147}$?  {Note:  If there is more than one excluded value use the word "and" between each excluded value.}

Accepted Answer

7

Question 5

Perform the indicated operation and reduce to lowest terms.  $\frac{12r^3+84r}{r+7} \cdot \frac{1}{8r^2}$

Accepted Answer

$\frac{3(r^2+7)}{2(r+7)}$

Question 6

Perform the indicated operation and reduce to lowest terms.  $\frac{8n-6}{9n+17}-\frac{n-8}{9n+17}$

Accepted Answer

$\frac{7n+2}{9n+17}$

Question 7

Perform the indicated operation and reduce to lowest terms.  $\frac{y-9}{2y+4}+\frac{y-7}{2}$

Accepted Answer

$\frac{y^2-4y-23}{2(y+2)}$

Question 8

Perform the indicated operations and reduce.  $\frac{7x^3-567x}{x^2+7x-18} \cdot (5x-10)$

Accepted Answer

$35x(x-9)$

Question 9

Perform the indicated operation and reduce to lowest terms.  $\frac{v-3}{9v-63}÷\frac{v-3}{4v-28}$

Accepted Answer

$\frac{4}{9}$

Question 10

Perform the indicated operation and reduce to lowest terms.  $\frac{\frac{r-7}{3}}{\frac{r^2-49}{6r+12}}$

Accepted Answer

$\frac{2(r+2)}{r+7}$

Question 11

Solve the equation.  Check for extraneous solutions.  $\frac{8x}{x-6}=9+\frac{48}{x-6}$

Accepted Answer

$\emptyset$

Question 12

Solve the equation and check for extraneous solutions.  $\frac{8}{5n+30}-\frac{3}{5}=\frac{7}{n+6}$

Accepted Answer

-15=n

Question 13

Which value of $x$ makes the expression $\frac{x+6}{x-8}$ undefined?

Accepted Answer

8

Answer

-6

Answer

-8

Answer

6

Question 14

What is the product of $\frac{7x}{x-2}$ and $\frac{x^2-4}{5x+10}$ expressed in simplest form?

Accepted Answer

$\frac{7x}{5}$

Answer

$\frac{7x^2}{5(x+2)}$

Answer

$\frac{7x^2}{5}$

Answer

$\frac{7(x+2)}{5}$

Question 15

Simplify the following rational expression to cancel out the $h$ in the denominator.  $\frac{[7(x+h)^2-8]-[7x^2-8]}{h}$

Accepted Answer

7h+14x

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