Algebraic Fractions Practice Questions

Write $\frac{3x + 2}{4} - \frac{x - 5}{6}$ as a single fraction.

Give your answer in its simplest form.

Simplify fully $\dfrac{x^{2} - 7x + 12}{x^{2} - 9}$

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

Give your answer in its simplest form.

Write $\dfrac{5x}{2x^{2} + x - 6} + \dfrac{3}{x + 2}$ as a single fraction.

Give your answer in its simplest form.

Simplify fully $\dfrac{4p^{2} - 25}{3p} \times \dfrac{12p}{10 - 4p}$

Simplify fully $\dfrac{x^{2} - 16}{3x + 6} \div \dfrac{4x - 16}{x^{2} - 4}$

Show that the expression simplifies to $\dfrac{k}{x + 3}$, where $k$ is an integer.

State the value of $k$.

Hence solve $\dfrac{4}{x - 4} - \dfrac{28}{x^{2} - x - 12} = \dfrac{1}{2}$

Solve $\dfrac{2x + 1}{x + 6} = \dfrac{x + 5}{x - 2}$

You must show your working.

Show that $g(\theta) = \dfrac{\tan\theta}{3}$

Hence solve $g(\theta) = -\dfrac{1}{3}$ for $90° < \theta < 180°$

You must show your working.