topic badge
iGCSE (2021 Edition)

13.04 Simplifying algebraic fractions

Worksheet
Simplify algebraic fractions
1

Simplify:

a

\dfrac{40 y}{450}

b

\dfrac{6 n}{9 n}

c

\dfrac{42 x y}{24 y}

d

\dfrac{15 n^{2}}{- 40 n}

e

\dfrac{64 m n^{2}}{40 m^{2} n}

f

-\dfrac{10 x^{2}}{6 xy^{3}}

g

\dfrac{6 p^{5}}{3 p^{3}}

h

\dfrac{10 a^{3}b^5}{25 a^{2}b^9}

2

Simplify:

a

\dfrac{25 x - 40}{55}

b

\dfrac{4 u v - 20 u w}{4 u}

c

\dfrac{5 u}{5 u v - 30 u w}

d

\dfrac{9 m^{2} + 24 m n}{18 m^{2}}

3

Simplify:

a

\dfrac{4 x + 20 y}{x + 5 y}

b

\dfrac{2 x - 6 y}{x - 3 y}

c

\dfrac{x - 2}{2 - x}

d

\dfrac{5 y - 30}{6 - y}

e

\dfrac{2 x + 6}{x^{2} + 3 x}

f

\dfrac{8 - 2 x}{5 x^{2} - 20 x}

g

\dfrac{10 x - 15}{2 x^{3} - 3 x^{2}}

h

\dfrac{8 - 2 x y}{x^{2} y - 4 x}

i

\dfrac{12 m^{2} + 6 m n}{18 m n + 36 m^{2}}

4

Simplify:

a
\dfrac{(x+3)(x-2)}{x+3}
b
\dfrac{(2x-5)(x+4)}{x+4}
c
\dfrac{x-7}{2(x-7)(x+4)}
d
\dfrac{(x+6)(x+8)}{(x+6)(x-9)}
e
\dfrac{x^2-8x+16}{x-4}
f
\dfrac{x^2 + 7x+12}{x+4}
g
\dfrac{x^2+9x+20}{(x+5)(x+1)}
h
\dfrac{x^2 - 3x -18}{(x-6)(x+2)}
5

Simplify:

a

\dfrac{m^{2} - 16}{m - 4}

b

\dfrac{m^{2} - 64}{8 + m}

c

\dfrac{x - 10}{x^{2} - 100}

d

\dfrac{a^{2} - 121}{11 - a}

6

Simplify:

a

\dfrac{8 \left(p - q\right)^{2}}{8 p^{2} - 8 q^{2}}

b

\dfrac{x + 10}{x^{2} + 20 x + 100}

c

\dfrac{x^{2} - 4 x + 4}{7 \left(x - 2\right)}

d

\dfrac{x^{2} + 8 x + 15}{x + 5}

e

\dfrac{x + 5}{x^{2} + 2 x - 15}

f

\dfrac{3 x^{2} - 18 x - 216}{4 \left(x + 6\right)}

g

\dfrac{3 y + 6}{y^{2} - 4}

h

\dfrac{m^{2} - 16}{5 m + 20}

i

\dfrac{x^{2} + 6 x + 9}{x^{2} - 9}

j

\dfrac{x^{2} - 3 x - 10}{x^{2} - 5 x}

k

\dfrac{x^{2} + 5 x + 6}{x^{2} - 2 x - 8}

l

\dfrac{8 \left(x + 3\right)}{5 x^{2} + 30 x + 45}

m

\dfrac{\left(x + 3\right) \left(x - 11\right)}{x^{2} - 18 x + 77}

n

\dfrac{4 x^{2} + 8 x - 192}{2 x + 16}

7

Simplify:

a

\dfrac{x y + 10 x + 9 y + 90}{x + 9}

b

\dfrac{5 \left(x - 12\right)}{x y + 6 x - 12 y - 72}

c

\dfrac{y - 8}{3 x y - 24 x - 30 y + 240}

d

\dfrac{5 x y - 20 x + 40 y - 160}{8 \left(y - 3\right) \left(y - 4\right)}

e

\dfrac{w x y + w x z}{w y + w z + x y + x z}

f

\dfrac{x^{2} - x y + x z - y z}{x^{2} - 2 x y + y^{2}}

8

Simplify the following algebraic fraction:\dfrac{5 \left(k^{2} - 5\right)^{4} + 20 k \left(k^{2} - 5\right)^{5}}{15 \left(k^{2} - 5\right)^{4}}

Sign up to access Worksheet
Get full access to our content with a Mathspace account

Outcomes

0607C2.9

Algebraic fractions: simplification, addition or subtraction of fractions with integer denominators, multiplication or division of two simple fractions.

0607E2.9

Algebraic fractions: simplification, including use of factorisation, addition or subtraction of fractions with linear denominators or single term, multiplication or division and simplification of two fractions.

What is Mathspace

About Mathspace