Chapter 8

Find the domain of \(\frac{5 a+1}{a^{2}-5 a-24}\).

For the following problems, find the domain of each rational expression. $$ \frac{9}{x+4} $$

Perform the following divisions. $$ \frac{2 x^{2}+x-1}{x} $$

Use the combine-divide method to simplify each expression. $$ \frac{\frac{27 x^{2}}{6}}{\frac{15 x^{3}}{8}} $$

The same number is added to the numerator and denominator of the fraction \(\frac{4}{9} .\) The result is \(\frac{2}{3} .\) What is the number that is added? Step 1: Let \(x=\) Step 2: Step 3: Step 4: Step 5: The number added is _______.

Solve the following rational equations. \(\frac{2 x}{5}=\frac{x-14}{6}\)

Find the domain of each of the following rational expressions. $$ \frac{2}{x-7} $$

Perform each multiplication. $$ \frac{5}{3} \cdot \frac{6}{7} $$

Determine \(\mathbf{N}\). $$ \frac{3}{8}=\frac{N}{48} $$

Add or Subtract the following rational expressions. $$ \frac{4}{9}+\frac{2}{9} $$

Reduce each of the following fractions to lowest terms. $$ \frac{30 y}{35 y} $$

For the following problems, fill in the missing term. -\frac{3}{x+4}=\frac{\underline{\phantom{xx}}}{x+4}$

Perform the following divisions. $$ \frac{3 x^{3}+4 x^{2}+10 x-4}{x^{2}} $$

For the following problems, find the domain of each rational expression. $$ \frac{10 x}{x+6} $$

Seven halves of a number added to the reciprocal of the number yields \(\frac{23}{6}\). What is the number? Step 1: Let \(x=\) Step 2: Step 3: Step 4: Step 5: The number is ________.

Use the combine-divide method to simplify each expression. $$ \frac{3-\frac{1}{x}}{3+\frac{1}{x}} $$

Solve the following rational equations. \(\frac{3 a}{a-1}=\frac{3 a+8}{a+3}\)

Find the domain of each of the following rational expressions. $$ \frac{5 x}{x(x+4)} $$

Perform each multiplication. $$ \frac{a^{3}}{b^{2} c^{2}} \cdot \frac{c^{5}}{a^{5}} $$

Add or Subtract the following rational expressions. $$ \frac{3}{b}+\frac{2}{b} $$

Reduce each of the following fractions to lowest terms. $$ \frac{x^{2}-9}{x^{2}+5 x+6} $$

$$ \frac{2 x+5}{-x+1}=\frac{\underline{\phantom{xx}}}{x-1} $$

Perform the following divisions. $$ \frac{a^{2} b+3 a b^{2}+2 b}{a b} $$

For the following problems, find the domain of each rational expression. $$ \frac{x+1}{2 x-5} $$

Person A, working alone, can pour a concrete walkway in 9 hours. Person B, working alone, can pour the same walkway in 6 hours. How long will it take both people to pour the concrete walkway working together? Step 1: Step 2: Step 3: Step 4: Step 5: Working together, \(\mathrm{A}\) and \(\mathrm{B}\) ______.

Use the combine-divide method to simplify each expression. $$ \frac{1+\frac{u}{y}}{x-\frac{y^{2}}{x}} $$

Solve the following rational equations. \(\frac{3}{y-3}+2=\frac{y}{y-3}\)

Find the domain of each of the following rational expressions. $$ \frac{2 x+1}{(x+2)(1-x)} $$

Perform each multiplication. $$ \frac{y-1}{y^{2}+1} \cdot \frac{y+1}{y^{2}-1} $$

Determine \(\mathbf{N}\). $$ \frac{-2 y}{y-1}=\frac{N}{y^{2}-1} $$

Add or Subtract the following rational expressions. $$ \frac{5 x}{2 y^{2}}-\frac{3 x}{2 y^{2}} $$

Reduce each of the following fractions to lowest terms. $$ \frac{x+2 b}{4 x+8 b} $$

For the following problems, perform the divisions. $$ \frac{y^{2}+4}{y+2} $$

For the following problems, reduce to lowest terms. $$ \frac{30 x^{6} y^{3}(x-3)^{2}(x+5)^{2}}{6 x y^{3}(x+5)} $$

Perform the following divisions. $$ \frac{14 x^{2} y^{2}-7 x y}{7 x y} $$

For the following problems, find the domain of each rational expression. $$ \frac{2 a+3}{7 a+5} $$

An inlet pipe can fill a water tank in 8 hours and an outlet pipe can drain the tank in 10 hours. If both pipes are open, how long will it take to fill the tank? Step 1: Step 2: Step 3: Step 4: Step 5:

Use the combine-divide method to simplify each expression. $$ \frac{m-3+\frac{2}{m}}{m-4+\frac{3}{m}} $$

Solve the equation \(\frac{a+3}{a-2}=\frac{a+1}{a-1}\).

Find the domain of each of the following rational expressions. $$ \frac{5 a+2}{a^{2}+6 a+8} $$

Perform each multiplication. $$ \frac{x^{2}-x-12}{x^{2}+7 x+6} \cdot \frac{x^{2}-4 x-5}{x^{2}-9 x+20} $$

Add or Subtract the following rational expressions. $$ \frac{x+2}{x-y}+\frac{2 x+3 u}{x-y} $$

Reduce each of the following fractions to lowest terms. $$ \frac{-3 a^{4}+75 a^{2}}{2 a^{3}-16 a^{2}+30 a} $$

For the following problems, perform the divisions. $$ \frac{y^{3}+3 y^{2}+4}{y+2} $$

$$ \frac{x^{2}+10 x+24}{x^{2}+x-30} $$

Perform the following divisions. $$ \frac{10 m^{3} n^{2}+15 m^{2} n^{3}-20 m n}{-5 m} $$

For the following problems, find the domain of each rational expression. $$ \frac{3 m}{2 m(m-1)} $$

It takes person A 4 hours less than person B to complete a certain task. Working together, both can complete the task in \(\frac{8}{3}\) hours. How long does it take each person to complete the task working alone? Step 1: Step 2: Step 3: Step 4: Step 5:

Use the combine-divide method to simplify each expression. $$ \frac{1+\frac{1}{x-1}}{1-\frac{1}{x-1}} $$

Find the domain of each of the following rational expressions. $$ \frac{12 y}{3 y^{2}-2 y-8} $$