wayground logo

Free Printable Worksheets

Font size

S
M
L
XL
Worksheets

Operations on Rational Expressions

Total questions: 11

Worksheet time: 33mins

Name
Class
Date
1.

Simplify:  36y72z\frac{36y}{72z}  

a)

 4y9z\frac{4y}{9z}  

b)

 y2z\frac{y}{2z}  

c)

 2y3z\frac{2y}{3z}  

d)

 18y38z\frac{18y}{38z}  

2.

Simplify: xyyx\frac{x-y}{y-x}  

a)

 xyyx\frac{x-y}{y-x}  

b)

 1x\frac{1}{-x}  

c)

 1-1  

d)

 1y\frac{-1}{y}  

3.

Simplify: b2b6b2+4b+4\frac{b^2-b-6}{b^2+4b+4}  

a)

 b6b+4\frac{b-6}{b+4}  

b)

 b+3b+2\frac{b+3}{b+2}  

c)

 b+3b+4\frac{b+3}{b+4}  

d)

 b3b+2\frac{b-3}{b+2}  

4.

Simplify: r3+j3r2ry+j2\frac{r^3+j^3}{r^2-ry+j^2}  

a)

 r+jrj\frac{r+j}{r-j}  

b)

 (r2+rj+j2)(r2j)\frac{\left(r^2+rj+j^2\right)}{\left(r-2j\right)}  

c)

 r+jr+j  

d)

 (r+j)(r2+rj+j2)(r2j)(r+j)\frac{\left(r+j\right)\left(r^2+rj+j^2\right)}{\left(r-2j\right)\left(r+j\right)}  

5.

Find the product: x4x+7×x3x8\frac{x-4}{x+7}\times\frac{x-3}{x-8}  

a)

 x27x+12x2x56\frac{x^2-7x+12}{x^2-x-56}  

b)

 x212x+32x2+4x21\frac{x^2-12x+32}{x^2+4x-21}  

c)

 x2+7x+12x256\frac{x^2+7x+12}{x^2-56}  

d)

 x212x+32x221\frac{x^2-12x+32}{x^2-21}  

6.

Find the product: a+ba3+b3×a2ab+b2ab\frac{a+b}{a^3+b^3}\times\frac{a^2-ab+b^2}{a-b}  

a)

 a+ba2b2\frac{a+b}{a^2-b^2}  

b)

 1ab\frac{1}{a-b}  

c)

 a+ba+b  

d)

1

7.

Find the quotient: a243a÷5a2a2\frac{a^2-4}{3a}\div\frac{5a^2}{a-2}  

a)

 5a(a+4)3\frac{5a\left(a+4\right)}{3}  

b)

 a32a24a+815a3\frac{a^3-2a^2-4a+8}{15a^3}  

c)

 5a2+20a3\frac{5a^2+20a}{3}  

d)

 a36a+815a\frac{a^3-6a+8}{15a}  

8.

Write this product in simplest form:
  6a2b15c35c4a\frac{6a^2b}{15c^3}\cdot\frac{5c}{4a}  

a)

 30a2bc60ac3\frac{30a^2bc}{60ac^3}  

b)

 a2bc2ac3\frac{a^2bc}{2ac^3}  

c)

 30a2bc60ac3\frac{30a^2bc}{60ac^3}  

d)

 ab2c2\frac{ab}{2c^2}  

9.

Write the following quotient in simplest form:

 8(p1)p+3÷p1p+3\frac{8\left(p-1\right)}{p+3}\div\frac{p-1}{p+3}  

a)

 88  

b)

 8p1p+3\frac{8p-1}{p+3}  

c)

 8(p1)(p+3)(p+3)(p1)\frac{8\left(p-1\right)\left(p+3\right)}{\left(p+3\right)\left(p-1\right)}  

d)

 8(p1)(p+3) + (p1)(p+3)(p+3)(p1)\frac{8\left(p-1\right)\left(p+3\right)\ +\ \left(p-1\right)\left(p+3\right)}{\left(p+3\right)\left(p-1\right)}  

10.

Write this product in simplest form:

 h2+3h24h+3\frac{h^2+3h}{2}\cdot\frac{4}{h+3}  

a)

 4(h2+3h)2(h+3)\frac{4\left(h^2+3h\right)}{2\left(h+3\right)}  

b)

 2h2+3hh+3\frac{2h^2+3h}{h+3}  

c)

 2h2h  

d)

 2(h2+3h)h+3\frac{2\left(h^2+3h\right)}{h+3}  

11.

Simplify

 x23x10x2+4x+4x2+7x+10x225\frac{x^2-3x-10}{x^2+4x+4}\cdot\frac{x^2+7x+10}{x^2-25}  

a)

 11  

b)

 2x2+4x2x2+4x21\frac{2x^2+4x}{2x^2+4x-21}  

c)

 00  

d)

 10x204x+29\frac{-10x-20}{4x+29}