Algebraic Fractions (AQA GCSE Further Maths): Exam Questions

Simplify fully $\frac{15x^{2}y-5x{y}^2}{12x-4y}$

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

You must show your working.

Circle the expression that is equivalent to    $\frac{1}{a}+\frac{1}{b}$

Simplify fully   $\frac{6c^4-c^3}{36c^2-1}$.

Simplify   $\frac{x^2-7x+10}{x^2-2x-15}$

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

Do not use trial and improvement. Write your solutions to 3 significant figures.

Show that  $\frac{x^4}{x+4}\times \frac{x+2}{x}÷\frac{x^2}{3x+12}$

simplifies to the form $a{x}^2+bx$ where $a$ and $b$ are integers.

Simplify    $\frac{8x^3-50x}{2x\left(6x^2-x-35\right)}$

Give your answer in the form   $\frac{ax+b}{cx+d}$   where $a,b,c$ and $d$ are integers.

Write

$\frac{9}{2x^2-x-1}-\frac{12}{4x^2-1}$

as a single algebraic fraction.

Give your answer fully simplified.

$\mathrm{f}\left(x\right)=\frac{x}{2x+1}$  for positive values of $x$.

Work out   $\mathrm{f}\left(x+1\right)-\mathrm{f}\left(x\right)$

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