Mathematics 0580 · IGCSE
Algebraic fractions
47 practice questions on Algebraic fractions, with worked solutions and instant marking.
Simplify the expression $\frac{ab - b^2}{a^2 - b^2}$.
Feb/March 2019
Simplify the expression $\frac{5x^2 - 19x + 12}{x^2 - 9}$.
Feb/March 2023
Express $\dfrac{x}{4} + \dfrac{3x}{8} - \dfrac{x+2}{12}$ as a single fraction in its simplest form.
Feb/March 2025
Express $\frac{3}{x+2} - \frac{4}{2x-5}$ as one fraction in simplest form.
May/June 2015
Express it as one fraction in simplest form: $\frac{2x - 1}{3} - \frac{2}{x + 1}$.
May/June 2017
Use algebra to simplify $\frac{3+x}{9-x^2}$.
May/June 2018
Express as a single fraction in its simplest form: $\frac{1}{y-1} - \frac{1}{y}$.
May/June 2018
Rewrite the expression as one fraction in simplest form: $\frac{1}{x+2} - \frac{2}{3x-1}$.
May/June 2019
Rewrite as a single fraction in its simplest form: $\frac{2x}{x+3} + \frac{x+3}{x-5}$.
May/June 2019
Simplify $\frac{x^3 + 5x^2}{x^2 - 25}$, and give your answer in the form of one fraction.
May/June 2019
Simplify the expression $\frac{2x^2 - 5x - 12}{3x^2 - 12x}$.
May/June 2021
Simplify the expression $\frac{5x - x^2}{25 - x^2}$.
May/June 2022
Rearrange the formula $c = \frac{3x}{2x - 5}$ so that $x$ is the subject.
May/June 2023
Express $\frac{5}{3x + 2} + \frac{4}{2x - 1}$ as one fraction and give it in simplest form.
May/June 2023
Simplify the fraction $\frac{2x^2 + 5x - 12}{4x^2 - 9}$.
May/June 2023
Find the simplified form of $\frac{2}{y+1} - \frac{3}{y}$. Write your answer as one fraction in lowest terms.
May/June 2024
Simplify the expression $\frac{pt - p - t + 1}{1 - t^2}$.
May/June 2024
Express the result as one fraction in lowest terms.
May/June 2025
Simplify the expression $\frac{7x - x^2}{49 - x^2}$.
May/June 2025
Simplify $\frac{x^2 - 16}{x^2 - 3x - 4}$.
Oct/Nov 2015
Express each of the following as one fraction.
Oct/Nov 2015
Simplify $\frac{4 + 10w}{8 - 50w^2}$.
Oct/Nov 2015
Factorise $x^2 - 3x - 10$.
Oct/Nov 2015
Express $1 - \dfrac{2}{p} - \dfrac{3}{t}$ as a single fraction.
Oct/Nov 2016
Simplify the fraction $\dfrac{42np - 7n}{12pr - 2t + 18mp - 3m}$.
Oct/Nov 2016
Express as one fraction in simplest form $\dfrac{5}{x-3} + \dfrac{3}{x+7} + \dfrac{1}{2}$.
Oct/Nov 2017
Write $\frac{x+1}{x} - \frac{y-1}{y}$ as one fraction and reduce it to simplest form.
Oct/Nov 2017
Write the expression as a single fraction in its simplest form: $\frac{x - 5}{3} + \frac{6}{x + 2}$.
Oct/Nov 2018
Express $\dfrac{1}{x} - \dfrac{1}{x+1}$ as a single fraction in simplest form.
Oct/Nov 2018
Simplify $\dfrac{2x^2 - x - 1}{2x^2 + x}$.
Oct/Nov 2018
Express $\frac{x}{2} - \frac{2x + 4}{x + 1}$ as one fraction, and give it in simplest form.
Oct/Nov 2019
Simplify $\frac{x^2 - 5x}{2x^2 - 50}$.
Oct/Nov 2020
Put into one fraction in its simplest form: $2 - \frac{2x - 1}{x + 1}$.
Oct/Nov 2020
Simplify the expression $\frac{ux - 2u - x + 2}{u^{2} - 1}$.
Oct/Nov 2020
Simplify $\frac{x^2 - 25}{x^2 - 17x + 60}$.
Oct/Nov 2020
Express as one fraction in the simplest form: $\frac{2}{x+3} - \frac{x+2}{7}$.
Oct/Nov 2021
Simplify $\frac{3xy + 36y - 5x - 60}{2x^2 - 288}$.
Oct/Nov 2021
Simplify this expression. $\dfrac{3x^{2} - 18x}{ax - 6a + 2cx - 12c}$
Oct/Nov 2021
Solve $\frac{4}{x+1}+\frac{2}{2x-5}=3$. You must present all your working.
Oct/Nov 2022
Expand the product and simplify $(2x - 1)(x + 4)(x - 3)$.
Oct/Nov 2022
Express as one fraction in lowest terms: $\frac{10x^2-60x}{x^2-x-30}$.
Oct/Nov 2023
Simplify the expression $\dfrac{ax - 2a - x + 2}{a^2 - 1}$.
Oct/Nov 2023
Simplify the expression $(64y^{27})^{\frac{2}{3}}$.
Oct/Nov 2023
Simplify $\dfrac{3x - 2 - 3xy + 2y}{1 - y^2}$.
Oct/Nov 2024
Simplify $\frac{10ax+6bx-25a-15b}{4x^2-25}$.
Oct/Nov 2025
Express your answer as one fraction, reduced fully.
Oct/Nov 2025
Simplify the expression.
Oct/Nov 2025