Free Printable Integrated Algebra Quiz - Dividing Rational Expressions

1.

Find the fully factored simplified quotient when you divide:

$\frac{x^2-2x-8}{x^2-2x-15}\$ by $\frac{2x^2-8x}{2x^2-10x}$

a)

$\frac{2\left(x-2\right)}{2\left(x+3\right)}\$

b)

$\frac{2\left(x+2\right)}{2\left(x+3\right)}\$

c)

$\frac{x-2}{x+3}\$

d)

$\frac{x+2}{x+3}\$

e)

$\frac{2x+4}{2x+6}$

2.

Find the fully factored simplified quotient when you divide:

$\frac{a^2-5a-14}{a-7}\$ by $\frac{a^2-a-6}{5a^3+30a^2}$

a)

$\frac{a+9}{15a}\$

b)

$\frac{5a^2\left(a+6\right)}{a-3}\$

c)

$\frac{1}{a-1}\$

d)

$\frac{9a}{a-3}\$

e)

$\frac{5a^3+30a^2}{a-3}$

3.

Find the fully factored simplified quotient when you divide:

$\frac{g+8}{6g+60}\$ by $\frac{g^2-64}{g^2+2g-80}$

a)

$\frac{1}{6}\$

b)

$\frac{g+8}{6g+60}\$

c)

$\frac{g+10}{6g+60}\$

d)

$6$

e)

$\frac{6}{6g+60}$

4.

Find the fully factored simplified quotient when you divide:

$\frac{2q^2-4q-6}{3q^3-9q^2}\$ by $\frac{4q^2+2q-2}{2q+1}$

a)

$\frac{1}{3q^2}\$

b)

$\frac{2q-1}{3q^2\left(2q+1\right)}\$

c)

$3q^2\$

d)

$\frac{2q+1}{6q^3-3q^2}$

e)

$\frac{2q+1}{3q^2\left(2q-1\right)}$

5.

Find the fully factored simplified quotient when you divide:

$\frac{3q^3-9q^2+5q-15}{q^2-9}\$ by $\frac{6q^3+10q}{q^2}$

a)

$\frac{q}{2\left(q+3\right)}\$

b)

$\frac{q}{2q+6}\$

c)

$\frac{2q+6}{2}\$

d)

$q$

e)

$\frac{1}{2q^2}$

6.

Find the fully factored simplified quotient when you divide:

$\frac{5n^2-33n-14}{8n^2+12n}\$ by $\frac{2n^2-17n+21}{4n^2-9}$

a)

$\frac{5n+2}{4n}\$

b)

$\frac{5n+2}{8n^2+12n}\$

c)

$\frac{n-7}{n}\$

d)

$5n+2$

e)

$\frac{4n}{5n+2}$

7.

Find the fully factored simplified quotient when you divide:

$\frac{5n^2+10n}{6n^2-24}\$ by $\frac{5n^2-22n-15}{n^2-7n+10}$

a)

$\frac{5n}{30n+18}\$

b)

$\frac{5n}{5n+3}\$

c)

$\frac{5n}{6\left(5n+3\right)}\$

d)

$\frac{5}{30n+18}$

e)

$\frac{5}{6\left(5n+3\right)}$

8.

Find the fully factored simplified quotient when you divide:

$\frac{q^2+6q+9}{4q^2+13q+3}\$ by $\left(7q^2+27q+18\right)$

a)

$\frac{1}{28q^2+31q+6}\$

b)

$\frac{1}{\left(4q+1\right)\left(7q+6\right)}\$

c)

$28q^2+31q+6$

d)

$\frac{q+3}{28q^2+31q+6}$

e)

$\frac{1}{7q+6^{ }}$

9.

Find the fully factored simplified quotient when you divide:

$\left(6a^2+5a-6\right)\$ by $\frac{2a^2+13a+15}{a^2-25}$

a)

$\left(3a-2\right)\left(a-5\right)$

b)

$3a^2-17a+10$

c)

$\frac{3a+2}{a^2-25}\$

d)

$\left(2a+3\right)\left(a+5\right)$

e)

$2a^2+17a+15$

10.

Which of the following statements are true when dividing rational expressions. Select all that apply.

a)

Flip the first rational expression

b)

Change division to multiplication

c)

Factor all numerators and denominators

d)

Keep the second rational expression the same

e)

Flip the second rational expression

Integrated Algebra Quiz - Dividing Rational Expressions

Total questions: 10

Worksheet time: 50mins

Similar Resources on Wayground