Free Printable Operations with Rational Expressions

1.

Simplify. State any restrictions on the variables $\frac{x^2-5x-24}{x^2-9}$

a)

$\frac{-5x-24}{-9}$ , $x\ne9$

b)

$\frac{\left(x-8\right)}{\left(x-3\right)},\ x\ne-3,\ 3,\ 8$

c)

$\frac{24}{9},\ x\ne-3,\ 3$

d)

$\frac{\left(x-8\right)}{\left(x-3\right)},\ x\ne-3,\ 3$

2.

Multiply. Simplify your result. All exponents in your answer have to be positive. State any restrictions on variables. $\frac{2x^4}{10y^{-5}}\cdot\frac{15y^3}{4x^6}$

a)

$\frac{3}{4}x^2y^2,\ x\ne0,\ y\ne0$

b)

$\frac{5}{4}x^{-2}y^2,\ x\ne0,\ y\ne0$

c)

$\frac{3y^8}{4x^2}$

d)

$\frac{3y^8}{4x^2},\ x\ne0,\ y\ne0$

3.

$\frac{\left(x^2-7x+10\right)}{\left(x^2-8x+15\right)}\div\frac{\left(x^2-4\right)}{\left(x^2+3x-18\right)}$ Divide. Simplify your answer. State any restrictions on the variables.

a)

$\frac{\left(x-2\right)^2\left(x+2\right)}{\left(x-3\right)^2\left(x+6\right)},\ x\ne-6,\ -2,\ 2,\ 3$

b)

$\frac{\left(x+9\right)}{\left(x+2\right)},\ x\ne-2,\ 3,\ 5,\ -9$

c)

$\frac{\left(x+6\right)}{\left(x+2\right)},\ x\ne-2,\ 2,\ 3,\ 5$

d)

$\frac{\left(x+6\right)}{\left(x+2\right)},\ x\ne-6,-2,\ 2,\ 3,\ 5$

4.

$\frac{\left(6x^3-6x^2\right)}{\left(x^4+5x^3\right)}\div\frac{\left(3x^2-15x+12\right)}{\left(2x^2+2x-40\right)}$ Check all that apply.

a)

$\frac{\left(6x^3-6x^2\right)}{\left(x^4+5x^3\right)}\cdot\frac{\left(2x^2+2x-40\right)}{\left(3x^2-15x+12\right)}$

b)

$\frac{6x^2\left(x-1\right)}{x^3\left(x+5\right)}\cdot\frac{\left(x+8\right)\left(x-10\right)}{\left(x-12\right)\left(x-3\right)}$

c)

$\frac{6x^2\left(x-1\right)}{x^3\left(x+5\right)}\cdot\frac{2\left(x+5\right)\left(x-4\right)}{3\left(x-4\right)\left(x-1\right)}$

d)

$\frac{4}{x},\ x\ne-5,\ 0,\ 1,\ or\ 4$

e)

$\frac{6x^2\left(x-1\right)}{x^3\left(x+5\right)}\cdot\frac{\left(x-4\right)\left(x+5\right)}{\left(x-4\right)\left(x-1\right)}$

5.

Check all that apply $\frac{\frac{3a^3b^3}{\left(a-b\right)}}{\frac{4ab}{\left(b-a\right)}}$

a)

$\frac{3a^3b^3}{\left(a-b\right)}\cdot\frac{\left(b-a\right)}{4ab}$

b)

$\frac{3a^3b^3}{\left(a-b\right)}\cdot\frac{4ab}{\left(a-b\right)}$

c)

$\frac{3a^2b^2}{4},\ a\ne0,\ b\ne0,\ a\ne b$

d)

$-\frac{3a^2b^2}{4},\ a\ne0,\ b\ne0,\ a\ne b$

6.

What is the sum of the two rational expressions in simplest form. State any restrictions on the variables.

\frac{x}{\left(x^2-4\right)}+\frac{1}{\left(x+2\right)}

a)

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

b)

$\frac{2x-2}{\left(x-2\right)\left(x+2\right)},\ x\ne\pm2$

c)

$\frac{2\left(x-1\right)}{\left(x-2\right)\left(x+2\right)},\ x\ne-2,\ 2$

d)

$\frac{2\left(x-1\right)}{\left(x^2-4\right)},\ x\ne\pm2$

e)

$\frac{x}{\left(x-2\right)},\ x\ne\pm2$

Operations with Rational Expressions

Total questions: 6

Worksheet time: 40mins

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