wayground logo

Free Printable Worksheets

NEW

Font size

S
M
L
XL
Worksheets

Rational Expressions: Simplify, Multiplication and Division

Total questions: 10

Worksheet time: 48mins

Name
Class
Date
1.

Simplify the expression below

 6y(y+3(y5))y(y5)(y1)\frac{6y\left(y+3\left(y-5\right)\right)}{y\left(y-5\right)\left(y-1\right)}  

a)

 6(y5)y(y1)\frac{6\left(y-5\right)}{y\left(y-1\right)}  

b)

 6y(y+3)y(y1)\frac{6y\left(y+3\right)}{y\left(y-1\right)}  

c)

 y(y1)6(y+3)\frac{y\left(y-1\right)}{6\left(y+3\right)}  

d)

 y(y+3)6y(y1)\frac{y\left(y+3\right)}{6y\left(y-1\right)}  

2.

simplify the expression below:

 4510a10\frac{45}{10a-10}  

a)

 92(a1)\frac{9}{2\left(a-1\right)}  

b)

 510a\frac{5}{10a}  

c)

 92(1a)\frac{9}{2\left(1-a\right)}  

d)

 52(a1)\frac{5}{2\left(a-1\right)}  

3.

For what values of x is  6x+4(x4)(x+5)\frac{6x+4}{\left(x-4\right)\left(x+5\right)}  undefined?

a)

x= 4 and x= 5

b)

x = 4 and x = -5

c)

x = -4 and x = 5

d)

x = 1  and x = -1

4.

Factor the following expression:
 (ab5b)\left(ab-5b\right)  

a)

 a (b5)a\ \left(b-5\right)  

b)

 b( 5a)b\left(\ 5-a\right)  

c)

 a(5b)a\left(5-b\right)  

d)

 b( a5)b\left(\ a-5\right)  

5.

Simplify the expression below:

 xy24xy(y4)(y+4)\frac{xy^2-4xy}{\left(y-4\right)\left(y+4\right)}  

a)

 x(y4)(y+4)\frac{x\left(y-4\right)}{\left(y+4\right)}  

b)

 xy(y4)y+4\frac{xy\left(y-4\right)}{y+4}  

c)

 xyy+4\frac{xy}{y+4}  

d)

 xyy4\frac{xy}{y-4}  

6.

Multiply the rational expressions

 35×163\frac{3}{5}\times\frac{16}{3}  =

a)

 65\frac{6}{5}  

b)

 125\frac{12}{5}  

c)

 410\frac{4}{10}  

d)

 165\frac{16}{5}  

7.

Divide the expression below:
 29÷413=\frac{2}{9}\div\frac{4}{13}=  

a)

 8117\frac{8}{117}  

b)

 1318\frac{13}{18}  

c)

 64\frac{6}{4}  

d)

 35\frac{3}{5}  

8.

Multiply the following rational expression:
 8x3x2y2 ×9x2y4a=\frac{8x}{3x^2y^2}\ \times\frac{9x^2y}{4a}=  

a)

 6xay\frac{6x}{ay}  

b)

 6a\frac{6}{a}  

c)

 9xy\frac{9x}{y}  

d)

 6x9y\frac{6x}{9y}  

9.

Divide the following rational expression:
 6xy38ab2÷3x2y4ab2=\frac{6xy^3}{8ab^2}\div\frac{3x^2y}{4ab^2}=  

a)

 y2y^2  

b)

 1x\frac{1}{x}  

c)

 x22y\frac{x^2}{2y}  

d)

 y2x\frac{y^2}{x}  

10.

Simplify the expression:
 (x+10)3x(x+10)=\frac{\left(x+10\right)}{3x\left(x+10\right)}=  

a)

 13x\frac{1}{3x}  

b)

 3x3x  

c)

 x+10x+10  

d)

 3x2+30x3x^2+30x