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iGCSE (2021 Edition)

13.06 Adding and subtracting algebraic fractions

Worksheet
Addition and subtraction of algebraic fractions
1

Simplify:

a

\dfrac{2 x}{7} + \dfrac{7 x}{7}

b

\dfrac{3x}{4}+\dfrac{2x}{4}

c

\dfrac{2 x}{3} + \dfrac{10 x}{3}

d

\dfrac{3 x}{12} + \dfrac{12 x}{12}

e

\dfrac{-8 x}{9} + \dfrac{4x}{9}

f

\dfrac{-3 x}{14} + \dfrac{- 2x}{14}

g

\dfrac{8 x}{2} - \dfrac{3 x}{2}

h

\dfrac{13x}{3}-\dfrac{8x}{3}

i

\dfrac{7 x}{5} - \dfrac{10 x}{5}

j

\dfrac{31 x}{6} - \dfrac{7 x}{6}

k

\dfrac{25 x}{24} - \dfrac{5 x}{24}

l
-\dfrac{4x}{7}-\dfrac{5x}{7}
2

Simplify:

a

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

b

\dfrac{7 x}{8} + \dfrac{5 x + 2}{8}

c

\dfrac{-2 x}{7} + \dfrac{4 x - 3}{7}

d
\dfrac{5x-1}{3}-\dfrac{2x+3}{3}
e

\dfrac{4 x - 10}{3} + \dfrac{- 5 x + 10}{3}

f

\dfrac{-6 x - 8}{5} + \dfrac{- 3 x -5}{5}

g
\dfrac{4x^2+11}{6}-\dfrac{3x^2-4x}{6}
h

\dfrac{2 x^2 - 3}{5} + \dfrac{3 x^2 + 6}{5}

i

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

j
\dfrac{2x-7x^3}{4}-\dfrac{-x^2-3x^3+1}{4}
3

Find the lowest common denominator for the following pairs of algebraic fractions:

a

\dfrac{w}{2} and \dfrac{w}{6}

b

\dfrac{s}{3} and \dfrac{s}{6}

c

\dfrac{x}{2} and \dfrac{y}{3}

d

\dfrac{r}{5} and \dfrac{s}{3}

4

Consider the algebraic fractions \dfrac{2 m}{5} and \dfrac{3 m}{6}.

a

Find the lowest common denominator.

b

Hence, simplify \dfrac{2 m}{5} + \dfrac{3 m}{6}.

5

Complete the following:

\dfrac{3x}{5}+\dfrac{2x}{⬚}=\dfrac{⬚}{35}
6

Simplify:

a

\dfrac{2 x}{5} + \dfrac{4 x}{7}

b

\dfrac{2 x}{14} + \dfrac{14 x}{21}

c
\dfrac{4x}{5}-\dfrac{x}{7}
d

\dfrac{4 x}{45} - \dfrac{x}{18}

e

- 9 x - \dfrac{5 x}{7}

f

\dfrac{3 x}{5} - \dfrac{2 x}{7}

g

-3x-\dfrac{3x}{8}

h

\dfrac{11x}{14}+\dfrac{7x}{21}

i

\dfrac{x}{15}+\dfrac{3x}{35}

j
\dfrac{4x^2}{3}-\dfrac{5x^2}{2}
7

Simplify:

a

\dfrac{2 x}{3} + \dfrac{2 x + 5}{9}

b

\dfrac{8 x}{13} + \dfrac{3 x + 4}{39}

c

\dfrac{3 x}{10} - \dfrac{4 x + 3}{16}

d

\dfrac{4x}{9}+\dfrac{2x-3}{36}

e

\dfrac{8 x}{11} - \dfrac{2 x - 3}{44}

f

\dfrac{y}{10}-\dfrac{5y+1}{25}

g

\dfrac{7 x}{8} - \dfrac{5 x + 6}{20}

h

\dfrac{x + 3}{3} + \dfrac{3 x - 2}{12}

i

\dfrac{x + 3}{3} - \dfrac{5 x - 7}{12}

j

\dfrac{2 x + 3}{4} - \dfrac{2 x + 2}{12}

k

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

l

\dfrac{3 x + 4}{6} + \dfrac{3 x + 4}{5}

m

\dfrac{2x+2}{4}-\dfrac{x+3}{8}

n

\dfrac{6x+7}{3}-\dfrac{3x-5}{9}

o

\dfrac{6 x^{2}}{7} + \dfrac{x^{2} + 5 x}{21}

p

\dfrac{2x^2}{7}+\dfrac{3x^2+2x}{28}

8

Simplify:

a
\dfrac{3}{x}+\dfrac{5}{y}
b
\dfrac{c}{ab}+\dfrac{2}{bc^2}
c
\dfrac{2x^2+4y}{y}-\dfrac{x-3}{x}
d
\dfrac{4}{x}+\dfrac{2}{x-2}
Extended
2

Simplify:

a

\dfrac{5}{x} + \dfrac{7}{x}

b

\dfrac{8}{3y} + \dfrac{10}{2y}

c

\dfrac{5 x - y}{x - 4} + \dfrac{x - 6 y}{4 - x}

d

\dfrac{5 x}{7 \left(x + 1\right)} - \dfrac{10}{x + 1}

e

\dfrac{1}{5} + \dfrac{7}{x - 6}

f

\dfrac{2 y + 5}{y - 3} - \dfrac{y + 3}{y - 3}

g
\dfrac{17}{6 t + 36} + \dfrac{14 + 3 t}{t + 6}
h

\dfrac{2}{\left(x + 3\right)} + \dfrac{5}{ \left(x + 5\right)}

i

\dfrac{x}{x-4} - \dfrac{12}{x + 4}

j
\dfrac{4}{x-5} + \dfrac{5}{x+8}
k

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

l

\dfrac{11 x}{x-2} - \dfrac{x + 5}{x+8}

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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.

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