Algebraic Fractions (Edexcel IGCSE Maths): Exam Questions

Write as a single fraction in its simplest form

$\frac{2}{y+3}-\frac{1}{y-6}$

Write $\frac{5}{x-3}-\frac{4}{x+3}$ as a single fraction in its simplest form.

Simplify $\frac{x+1}{2}+\frac{x+3}{3}$

Simplify $\frac{4 ( x + 5 )}{x^{2} + 2 x - 15}$

Simplify $\frac{3 ( x + 1 )}{( x + 1 )^{2}}$

Express

$\frac{3}{x}+\frac{x+2}{2x}+\frac{1}{4}$

as a single fraction in its simplest form.

Express $\frac{4}{x-2}-\frac{3}{x+1}$ as a single fraction.

Give your answer in its simplest form.

Write $\frac{2x+1}{4}+\frac{x-2}{3}$ as a single fraction in its simplest form.

Write as a single fraction $\frac{2}{3x}+\frac{4}{5x}-\frac{9}{10x}$

Give your answer in its simplest form.

Simplify fully $\frac{10x^{2}+23x+12}{4x^{2}-9}$

Simplify $\frac{3}{x}+\frac{4}{x}$ Circle your answer.

Simplify $\frac{25a}{8}\times\frac{2a}{5}$

Give your answer as a single fraction in its simplest form.

Show that, for $x\neq0$

$\frac{x+4}{3x}-\frac{5}{2x}$

can be written in the form $\frac{ax+b}{cx}$ where $a$, $b$ and $c$ are integers.

Circle the expression that is equivalent to $\frac{3x^{2}}{6x^{2}+3}$

Write as a single fraction in its simplest form.

$\frac{3}{x-1}+\frac{4}{x+2}$

Express as a single fraction.

$\frac{m+1}{n+1}-\frac{m}{n}$

Simplify your answer.

Solve $\frac{3x-2}{5}-\frac{3-4x}{2}=2$

Show clear algebraic working.

Express $\frac{3}{4}+\frac{5-x}{6x}$ as a single fraction in its simplest terms.

Simplify fully $\frac{2x^{2}-5x+3}{x^{2}+5x-6}$

Write as a single fraction in its simplest form $\frac{5}{2-x}-\frac{4}{x}$

Simplify $\frac{x^{2}-16}{2x^{2}-5x-12}$

Simplify fully $\frac{3x^{2}-8x-3}{2x^{2}-6x}$

Show that $\frac{2x^{2}-3x-5}{x^{2}+6x+5}$ can be written in the form $\frac{ax+b}{cx+d}$ where $a,b,c$ and $d$ are integers.

Simplify fully $\frac{x^{2}+3x-4}{2x^{2}-5x+3}$

Write $\frac{4}{x+2}+\frac{3}{x-2}$ as a single fraction in its simplest form.

Show that $\frac{a}{b + 1} - \frac{a}{( b + 1 )^{2}}$ can be written as $\frac{a b}{( b + 1 )^{2}}$

Simplify $\frac{x^{2}-9}{2x^{2}+5x-3}$

Solve $\frac{4-3x}{5}-\frac{3x-5}{2}=-3$

Show clear algebraic working.

$x$ = .......................

Solve the equation

$\frac{5}{x+2}+\frac{3}{x^{2}+2x}=2$

Show clear algebraic working.

Simplify fully $\frac{x^{5}-4x^{3}}{3x-6}$

Show that, for $x\neq--1$

$\frac{8x^{2}-8}{4x+4}$ simplifies to the form $ax+b$ where $a$ and $b$ are integers.

Show that $\frac{x+9}{x^{2}-1}+\frac{4}{x+1}$ can be written in the form $\frac{a}{x-1}$ where $a$ is an integer.

Show that $\frac{5 x}{x + 5} + \frac{25}{x - 7} - \frac{300}{( x + 5 ) ( x - 7 )}$ simplifies to an integer.

Solve

$\frac{1-2y}{3}=\frac{4}{5}-\frac{2y-1}{2}$

Show clear algebraic working

Write $\frac{2}{4 x - 3} - ( x + 4 ) \div ( \frac{2 x^{2} + 13 x + 20}{5} )$ as a single fraction in its simplest form. Show clear algebraic working.

$2-\frac{x+2}{x-3}-\frac{x-6}{x+3}$ can be written as a single fraction in the form $\frac{ax+b}{x^{2}-9}$

where $a$and $b$ are integers.

Work out the value of $a$ and the value of $b$.

Show that $\frac{1}{6x^{2}+7x-5}\div\frac{1}{4x^{2}-1}$ simplifies to $\frac{ax+b}{cx+d}$ where $a,b,c$ and $d$ are integers.

Simplify fully $\frac{3-x}{3x^{2}-5x-12}$

Write $\frac{x}{x-1}-\frac{x}{x+1}$ as a single fraction in its simplest form.

Write

$4 - [ ( x + 3 ) \div \frac{x^{2} + 5 x + 6}{x - 2} ]$

as a single fraction in its simplest form. You must show your working.

Show that $\frac{3x+6}{x^{2}-3x-10}\div\frac{x+5}{x^{3}-25x}$ simplifies to $ax$ where $a$ is an integer.

Show that $6 + [ ( x + 5 ) \div \frac{x^{2 } + 3 x - 10}{x - 1} ]$ simplifies to $\frac{ax-b}{cx-d}$ where $a,b,c$ and $d$ are integers.

Write $\frac{25 x^{2} - 64}{5 x^{2} - 13 x - 6} \times \frac{x^{2} - 8 x + 15}{5 x + 8} - ( x - 7 )$

as a single fraction in its simplest form.

Show clear algebraic working.

Given that $x=\frac{5}{9y+5}$ and that $y=\frac{5}{5a-2}$

find an expression for $x$ in terms of $a$.

Give your expression as a single fraction in its simplest form.

Express $\frac{1}{9x^{2}-25}-\frac{1}{6x+10}$ as a single fraction in its simplest form.

Simplify $\frac{2^{n}-1}{4^{n}-1}$

The flight of a plane was in two stages.

The table shows information about the flight.

In total, the flight lasted 2 hours. Work out the value of $x$.

Solve $\frac{5}{4x+1}=\frac{2x}{x^{2}+3}$

Give your solutions to 3 significant figures.

You must show your working.

Solve $\frac{x}{x+4}+\frac{7}{x-2}=1$

You must show your working.

$x$=.....................

Solve $\frac{x}{4}-\frac{2x}{x+2}=1$

Give your solutions to 2 decimal places. You must show your working.

Solve this equation, giving your answers correct to 1 decimal place.

$\frac{5}{x+2}+\frac{3}{x-3}=2$

$x$ = ........... or $x$ = ...........

Write $\frac{5}{4 x^{2} - 25} - ( 2 x + 3 ) \div ( \frac{4 x^{2} + 16 x + 15}{7} )$ as a single fraction in its simplest form.

Show clear algebraic working

Solve $\frac{45 x^{3} - 80 x}{3 x^{2} + x - 4} \times ( \frac{1}{3 x - 4} + \frac{1}{x} ) = \frac{4 ( x + 2 )}{5 x - 8}$

Show clear algebraic working.