Algebraic Fractions Practice Questions

Simplify fully $\dfrac{10x^2-4x}{2x}$

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

Simplify fully $\dfrac{4x+20}{x^2+10x+25}$

Simplify fully $\dfrac{2x^2-7x-15}{x^2-4x-5}$

Write $\dfrac{x^2-2x-8}{x^2-4}\times\dfrac{3x+6}{x-4}$ in the form $\dfrac{ax+b}{cx+d}$, where $a$, $b$, $c$ and $d$ are integers.

Find an expression for the length of the rectangle. Give your answer as a single fraction in its simplest form.

Simplify fully $\dfrac{2x^2+7x+3}{x^2-9}\div\dfrac{4x+2}{x^2-3x}$

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

Express $\dfrac{1}{x}+\dfrac{2}{x-1}-\dfrac{3}{x+1}$ as a single fraction in its simplest form.

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

Show clear algebraic working.

$\dfrac{5}{x-4}+2-\dfrac{x}{x+1}$ can be written as a single fraction in the form $\dfrac{x^2+bx+c}{(x-4)(x+1)}$, where $b$ and $c$ are integers.

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

$b =$ ______

$c =$ ______

Solve $\dfrac{2x}{x+3}-\dfrac{1}{x-1}=1$

You must show all your algebraic working.