# Algebra - Adding and Subtracting Algebraic Fractions 1

a - answer    s - solution    v - video    d - discussion

## Question 1

Express as a single fraction

a) $\dfrac x3+\dfrac x3$a s v d
b) $\dfrac x5+\dfrac{2x}{5}$a s v d
c) $\dfrac{2y}{9}+\dfrac{5y}{9}$a s v d
d) $\dfrac{2x}{9}+\dfrac{x}{9}$a s v d
e) $\dfrac{3z}{8}+\dfrac{z}{8}$a s v d
f) $\dfrac{2k}{11}+\dfrac{9k}{11}$a s v d
g) $\dfrac{5a}{6}+\dfrac{2a}{6}$a s v d
h) $\dfrac{9p}{4}+\dfrac{5p}{4}$a s v d

## Question 2

Express as a single fraction

a) $\dfrac{3x}{5}-\dfrac x5$a s v d
b) $\dfrac{6x}{7}-\dfrac{4x}{7}$a s v d
c) $\dfrac{9x}{10}-\dfrac{3x}{10}$a s v d
d) $\dfrac{3y}{4}-\dfrac{y}{4}$a s v d
e) $\dfrac{6m}{5}-\dfrac{m}{5}$a s v d
f) $\dfrac{7h}{3}-\dfrac{2h}{3}$a s v d
g) $\dfrac{7a}{2}-\dfrac{3a}{2}$a s v d
h) $\dfrac{8y}{5}-\dfrac{y}{5}-\dfrac{3y}{5}$a s v d

## Question 3

Express as a single fraction

a) $\dfrac x2+\dfrac x4$a s v d
b) $\dfrac x3+\dfrac x9$a s v d
c) $\dfrac{3x}{5}+\dfrac{x}{10}$a s v d
d) $\dfrac{5x}{8}+\dfrac{x}{4}$a s v d
e) $\dfrac{x}{10}+\dfrac{x}{2}$a s v d
f) $\dfrac{2g}{3}+\dfrac{g}{6}$a s v d
g) $\dfrac{13n}{15}+\dfrac{2n}{5}$a s v d
h) $\dfrac{11p}{20}+\dfrac{9p}{2}$a s v d

## Question 4

Express as a single fraction

a) $\dfrac x2-\dfrac x4$a s v d
b) $\dfrac x3-\dfrac x9$a s v d
c) $\dfrac{4v}{5}-\dfrac{v}{10}$a s v d
d) $\dfrac{9z}{10}-\dfrac{3z}{20}$a s v d
e) $\dfrac{7h}{6}-\dfrac{5h}{18}$a s v d
f) $\dfrac{2e}{7}-\dfrac{2e}{35}$a s v d
g) $\dfrac{8w}{3}-\dfrac{29e}{30}$a s v d
h) $\dfrac{5y}{6}-\dfrac{5y}{12}-\dfrac{y}{24}$a s v d

## Question 5

Express as a single fraction

a) $\dfrac x2+\dfrac x3$a s v d
b) $\dfrac x3+\dfrac x4$a s v d
c) $\dfrac{2x}{5}+\dfrac x4$a s v d
d) $\dfrac{2y}{7}+\dfrac{2y}{3}$a s v d
e) $\dfrac{2k}{3}+\dfrac{2k}{5}$a s v d
f) $\dfrac{m}{2}+\dfrac{m}{3}+\dfrac m4$a s v d
g) $\dfrac{3h}{4}+\dfrac{5h}{6}$a s v d
h) $\dfrac{5p}{8}+\dfrac{5p}{12}$a s v d

## Question 6

Express as a single fraction

a) $\dfrac x3-\dfrac x4$a s v d
b) $\dfrac x5-\dfrac x9$a s v d
c) $\dfrac{2x}{6}-\dfrac{x}{8}$a s v d
d) $\dfrac{3q}{2}-\dfrac{2q}{5}$a s v d
e) $\dfrac{7h}{3}-\dfrac{7h}{10}$a s v d
f) $\dfrac{3b}{4}-\dfrac{7b}{10}$a s v d
g) $\dfrac{11v}{2}-\dfrac{10v}{9}$a s v d
h) $\dfrac{7xy}{4}-\dfrac{2yx}{3}$a s v d

## Question 7

Express as a single fraction

a) $\dfrac{x+1}{2}+\dfrac{x}{2}$a s v d
b) $\dfrac{3x+2}{4}+\dfrac{2x+1}{4}$a s v d
c) $\dfrac{3x+2}{5}-\dfrac{2x}{5}$a s v d
d) $\dfrac{3x+5}{10}-\dfrac{x+1}{10}$a s v d
e) $\dfrac{x}{2}+\dfrac{x+1}{4}$a s v d
f) $\dfrac{x+1}{5}+\dfrac{3x}{10}$a s v d
g) $\dfrac{x+1}{2}-\dfrac{2x+1}{6}$a s v d
h) $\dfrac{2x+3}{5}-\dfrac{3x+2}{20}$a s v d

## Question 8

Express as a single fraction

a) $\dfrac{x+1}{2}+\dfrac{x}{3}$a s v d
b) $\dfrac{2x+1}{5}+\dfrac{x+1}{2}$a s v d
c) $\dfrac{3x}{4}+\dfrac{2x+3}{3}$a s v d
d) $\dfrac{5x+1}{4}-\dfrac{x}{6}$a s v d
e) $\dfrac{2x+1}{3}-\dfrac{3x}{5}$a s v d
f) $\dfrac{6x-1}{7}-\dfrac{x+2}{2}$a s v d
g) $\dfrac{2+p}{5}+\dfrac{8-p}{6}$a s v d
h) $\dfrac{x^2+x}{8}-\dfrac{2+x}{10}$a s v d

## Question 9

Express as a single fraction

a) $\dfrac{2x+1}{2}-\dfrac{x-1}{2}$a s v d
b) $\dfrac{2x-5}{5}-\dfrac{x-8}{5}$a s v d
c) $\dfrac{x+1}{2}-\dfrac{x-1}{4}$a s v d
d) $\dfrac{2x+3}{3}-\dfrac{2x-1}{9}$a s v d
e) $\dfrac{5x+3}{2}-\dfrac{2x-2}{3}$a s v d
f) $\dfrac{4x+1}{4}-\dfrac{x-4}{6}$a s v d
g) $\dfrac{2x+6}{5}-\dfrac{3-x}{2}$a s v d
h) $\dfrac{x^2-2x-3}{3}-\dfrac{x^2-5x-8}{7}$a s v d

## Question 10

Express as a single fraction

a) $\dfrac{3}{x}+\dfrac{5}{x}$a s v d
b) $\dfrac{4}{y}-\dfrac{2}{y}$a s v d
c) $\dfrac{3q}{p}-\dfrac{q}{p}$a s v d
d) $\dfrac{14}{xyz}-\dfrac{3}{xyz}$a s v d
e) $\dfrac{7v}{9u}-\dfrac{2v}{9u}$a s v d
f) $\dfrac{3xy}{a}-\dfrac{xy}{a}$a s v d
g) $\dfrac{4x}{xy}-\dfrac{2x}{xy}$a s v d
h) $\dfrac{5q}{spq}-\dfrac{4q}{sqp}$a s v d

## Question 11

Express as a single fraction

a) $\dfrac{1}{2x}+\dfrac{3}{x}$a s v d
b) $\dfrac{2}{6w}+\dfrac{1}{2w}$a s v d
c) $\dfrac{x}{2y}+\dfrac{x}{3y}$a s v d
d) $\dfrac{3}{2a}-\dfrac{4}{5a}$a s v d
e) $\dfrac{y}{x}-\dfrac{3y}{10x}$a s v d
f) $\dfrac{x+1}{2e}-\dfrac{x}{3e}$a s v d
g) $\dfrac{x+1}{2t}-\dfrac{2x-1}{7t}$a s v d
h) $\dfrac{3e+1}{6de}-\dfrac{5-2e}{7ed}$a s v d

## Question 12

Express as a single fraction

a) $\dfrac{2}{x}+\dfrac{3}{xy}$a s v d
b) $\dfrac{5}{y}-\dfrac{2}{xy}$a s v d
c) $\dfrac{3}{x}+\dfrac{5}{y}$a s v d
d) $\dfrac{2}{a}-\dfrac{3}{b}$a s v d
e) $\dfrac{q}{p}-\dfrac{q}{3p}$a s v d
f) $\dfrac{c}{3a}-\dfrac{2c}{b}$a s v d
g) $\dfrac{1}{4x}+\dfrac{8}{3y}$a s v d
h) $\dfrac{9c}{5ab}-\dfrac{8b}{7cd}$a s v d

## Question 13

Express as a single fraction

a) $\dfrac{y+1}{3x}+\dfrac{2}{3}$a s v d
b) $\dfrac{x+2}{3x}+\dfrac{3}{2}$a s v d
c) $\dfrac{2+x}{x}+\dfrac{x+3}{x^2}$a s v d
d) $\dfrac{6+p}{2p}-\dfrac{12}{p^2}$a s v d
e) $\dfrac{b}{3a}-\dfrac{5+b}{3a^3}$a s v d
f) $\dfrac{m^2-2m}{5m^2}-\dfrac{5}{3m}$a s v d
g) $\dfrac{x-2}{4x}-\dfrac{y-3}{6y}$a s v d
h) $\dfrac{2-p}{5p^2q}-\dfrac{18-q}{3q}$a s v d

## Question 14

Express as a single fraction

a) $\dfrac{3}{x}+\dfrac{2}{x+1}$a s v d
b) $\dfrac{3}{y}+\dfrac{5}{y-1}$a s v d
c) $\dfrac{4}{z+2}-\dfrac{8}{z}$a s v d
d) $\dfrac{5}{n+2}-\dfrac{1}{n^2}$a s v d
e) $\dfrac{4}{k^2-1}+\dfrac{6}{k^2}$a s v d
f) $\dfrac{1}{c+3}+\dfrac{4}{c+2}$a s v d
g) $\dfrac{3}{p+3}-\dfrac{1}{p-2}$a s v d
h) $\dfrac{2}{(x+1)(x+2)}-\dfrac{1}{(x+1)(x+3)}$a s v d

## Question 15

Express as a single fraction

a) $\dfrac{x+2}{x}+\dfrac{x}{x+1}$a s v d
b) $\dfrac{2x}{x+4}-\dfrac{x+1}{x}$a s v d
c) $\dfrac{5}{4+y}+\dfrac{y-3}{2y}$a s v d
d) $\dfrac{q+3}{q-2}+\dfrac{q+2}{q+1}$a s v d
e) $\dfrac{2x+7}{3x-1}-\dfrac{x+1}{x+5}$a s v d
f) $\dfrac{5x+6}{x+1}-\dfrac{x-3}{3x+2}$a s v d
g) $\dfrac{x-6}{4x-5}-\dfrac{2x-5}{2x-1}$a s v d
h) $\dfrac{3x-8}{2x-7}-\dfrac{5x-2}{4x-1}$a s v d