Free Printable Dividing Rational Expressions Practice

1.

Simplify and state the restrictions on the domain

\frac{10x-60}{x^2-36}\div\frac{4x-20}{x+6}

a)

$\frac{2x}{7\left(x+8\right)}\ \ \ \ \ \ \ \ x\ne-8$

b)

$\frac{2}{x}\ \ \ \ \ \ \ x\ne0$

c)

$\frac{5}{2\left(x-5\right)}\ \ \ \ \ \ \ \ \ \ \ x\ne6,\ -6,\ 5$

d)

$\frac{x-2}{14}\ \ \ \ \ \ \ none$

2.

Simplify and state the restrictions on the domain.

\frac{n^2+6n+5}{n^2+13n+36}\ \cdot\ \frac{3n+27}{3n+15}

a)

$\frac{n+1}{n+4}\ \ \ \ \ \ \ \ \ n\ne-9,\ -4,\ -5$

b)

$\frac{90n^3}{n+5}\ \ \ \ \ \ \ \ \ \ \ n\ne-5$

c)

$\frac{49n^2}{n-3}\ \ \ \ \ \ \ n\ne3$

d)

$3\ \ \ \ n\ne0$

3.

$\frac{x-2}{x^2-12x+20}\ \div\ \frac{x^2+3x-70}{10x-100}$

Simplify and state the restrictions on the domain.

a)

$\frac{9}{8}\ \ \ \ \ \ \ none$

b)

$\frac{x-6}{6x^2}\ \ \ \ \ \ \ \ \ x\ne0$

c)

$\frac{10\left(x-8\right)}{x-9}\ \ \ \ \ \ \ x\ne9$

d)

$\frac{10}{\left(x-7\right)\left(x+10\right)}\ \ \ \ \ \ \ \ \ \ x\ne10,\ 2,\ 7,\ -10$

4.

Simplify:

\frac{x^2-64}{x+8}\div\frac{x-8}{10}

a)

$\frac{x+7}{3x}$

b)

$10$

c)

$x-5$

d)

$x+3$

5.

$Simplify:\ \ \frac{k^2-36}{6k^2}\div\frac{k^2-36}{5k^2}$

a)

$\frac{k+9}{2}$

b)

$20k^3$

c)

$\frac{10}{k+10}$

d)

$\frac{5}{6}$

6.

$Simplify:\ \ \frac{10}{r^2+5r-24}\div\frac{1}{r+8}$

a)

$5$

b)

$\frac{7}{r-6}$

c)

$\frac{10}{r-3}$

d)

$\frac{6r^2}{\left(r+1\right)^2}$

7.

$Simplify:\ \ \ \frac{1}{n-2}\div\frac{n-8}{n^2-6n-16}$

a)

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

b)

$\frac{n-2}{7\left(n+4\right)}$

c)

$\frac{3}{8}$

d)

$\frac{n+2}{n-2}$

8.

$Simplify:\ \ \frac{1}{v+2}\div\frac{v+9}{v^2-v-90}$

a)

$\frac{v-9}{5v}$

b)

$3$

c)

$\frac{v-10}{v+2}$

d)

$\frac{9}{2}$

9.

a)

$\frac{x-8}{3x}$

b)

$\frac{3x}{x-8}$

c)

$\frac{3x}{x+8}$

d)

$\frac{x+8}{3x}$

10.

a)

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

b)

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

c)

$x+6$

Dividing Rational Expressions Practice

Total questions: 10

Worksheet time: 3hrs 30mins

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