Algebraic Fractions (Cambridge (CIE) IGCSE Maths: Extended): Non-Calculator Questions

Write as a single fraction in its simplest form.

$\frac{3}{x-4}-\frac{4}{x+3}$

Simplify.

$\frac{x^2-5x}{2x^2-50}$

Write as a single fraction in its simplest form.

$2-\frac{2x-1}{x+1}$

Write as a single fraction in its simplest form.

$\frac{x+3}{x-3}-\frac{x-2}{x+2}$

Write as a single fraction in its simplest form. 

$\frac{2x}{x+3}+\frac{x+3}{x-5}$ 

Simplify $\frac{x^3+5x^2}{x^2-25}$, giving your answer as a single fraction.

Write as a single fraction in its simplest form.

$\frac{5}{x-2}-\frac{x-5}{2}$

$\frac{3}{m+4}-\frac{4}{m}=6$

Show that this equation can be written as  $6m^2+25m+16=0$ .

Solve $\frac{7}{x+1}+\frac{4}{x+4}=3$

Show that the equation $\frac{7}{x+1}+\frac{4}{x+4}=3$ simplifies to $3x^2+4x-20=0$

Hence, or otherwise, solve $\frac{7}{x+1}+\frac{4}{x+4}=3$

Simplify.

$\frac{ux-2u-x+2}{u^2-1}$

$\mathrm{f}\left(x\right)=3x+2$  and  $\mathrm{g}\left(x\right)=x^2+1$.

Find $\frac{\mathrm{g}\left(x\right)}{\mathrm{f}\left(x\right)}+x$.
Give your answer as a single fraction, in terms of $x$, in its simplest form.

Simplify fully    $\frac{3-x}{3x^2-5x-12}$

Write  $\frac{x}{x-1}-\frac{x}{x+1}$ as a single fraction in its simplest form.