Mathematics 4024 · O Level
Algebraic fractions
29 practice questions on Algebraic fractions, with worked solutions and instant marking.
Put $\frac{1}{x}+2-\frac{3}{x+1}$ into a single fraction in simplest form.
May/June 2015
Solve the equation $\frac{7x}{4 - 3x} = 3$.
May/June 2017
Solve $\frac{4}{x-11}=\frac{1}{3x}$.
May/June 2018
Write $ rac{2}{3a}+ rac{5}{2a}$ as one fraction in lowest terms.
May/June 2018
Express $\frac{6y}{35} \div \frac{10y^2}{7}$ as a fraction in simplest form.
May/June 2019
Write as one fraction in simplest form: $\dfrac{3}{x - 7} + \dfrac{2}{x + 5}$.
May/June 2021
The algebraic fraction $\dfrac{2x^2 - 5x + a}{x^2 - 16}$ may be reduced to $\dfrac{2x + b}{x + 4}$.
May/June 2021
Solve for $x$: $\frac{2-5x}{3x+10}=3$.
May/June 2022
Solve $ rac{5x}{x-3}=x+4$.
May/June 2023
Solve $\dfrac{x}{x-1} - \dfrac{5}{x-3} = 1$.
May/June 2024
$r = \frac{4p + 3t}{2}$. Determine $p$ when $r = 10$ and $t = -2$.
May/June 2024
Simplify the expression $\dfrac{3x^2-12}{2x^2+11x+14}$.
May/June 2025
Simplify the expression $\frac{x^2 - 9}{5x^2 - 11x - 12}$.
May/June 2025
Write $\frac{5}{2x+1} - \frac{2}{4x-3}$ as one fraction in simplest form.
May/June 2025
Solve the equation $\frac{3x}{x-1} + \frac{4}{x+2} = 3$.
May/June 2025
Evaluate the value of $2^3 - 2^0$.
Oct/Nov 2016
Solve $\frac{y}{2y + 3} = \frac{2}{y + 5}$.
Oct/Nov 2017
Express the expression as a single fraction in simplest form: $\frac{4}{2x-3} - \frac{3}{x-2}$.
Oct/Nov 2018
Combine as a single fraction in simplest form $\dfrac{3}{y-1} - \dfrac{5}{y+6}$.
Oct/Nov 2018
Expand and simplify the expression $(x + 5)(x - 2)$.
Oct/Nov 2021
Solve the equation $3x-8=7$.
Oct/Nov 2021
Simplify the expression $\dfrac{x^2 - 4x}{x^2 - x - 12}$.
Oct/Nov 2022
Factorise the expression $6a - 9$.
Oct/Nov 2023
Solve the equation $\dfrac{3x}{x + 1} - \dfrac{2}{x - 1} = 3$.
Oct/Nov 2023
Express the expression below as a single fraction in its simplest form: $\dfrac{x+1}{8} + \dfrac{3x}{4} - \dfrac{5x}{16}$.
Oct/Nov 2023
Simplify $\dfrac{2x^{2} + 5x - 3}{2x^{2} + 6x}$.
Oct/Nov 2024
Solve $\dfrac{x}{x-1} - \dfrac{3}{2x-1} = 1$
Oct/Nov 2024
Express $\frac{5}{2x}-\frac{4}{7x}$ as a single fraction in simplest form.
Oct/Nov 2025
Express the result as one fraction in lowest terms.
Oct/Nov 2025