Algebraic Fractions (Cambridge (CIE) O Level Maths): Exam Questions

Simplify.

$\frac{5p^2-20p}{2p^2-32}$

Simplify $\frac{x^2-25}{x^2-17x+60}$.

$\mathrm{f}\left(x\right)=7x-4$  and  $\mathrm{g}\left(x\right)=\frac{2x}{x-3},x\ne 3$ 

Find $\frac{\mathrm{f}\left(x\right)}{2}+\mathrm{g}\left(x\right)$.
Give your answer as a single fraction, in terms of $x$, in its simplest form.

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

Solve.

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

Show all your working and give your answers correct to 2 decimal places.

$x$ = .......................... or $x$ = .......................... 

$\mathrm{f}\left(x\right)=\frac{3}{x+2},x\ne -2$  and  $\mathrm{g}\left(x\right)=8x-5$.  

Write  $\mathrm{g}\left(x\right)-\mathrm{f}\left(x\right)$ as a single fraction in its simplest form.

Simplify.

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

Simplify $\frac{y^2-9}{2y^2-y-15}$

Simplify $\frac{2x^2+x-15}{ax+3a-2bx-6b}$.

A car completes a 200 km journey at an average speed of $x$ km/h.
The car completes the return journey of 200 km at an average speed of $(x+10)$ km/h.

i) Show that the difference between the time taken for each of the two journeys is  $\frac{2000}{x(x+10)}$ hours.

[3]

ii) Find the difference between the time taken for each of the two journeys when $x=80$.
Give your answer in minutes and seconds.  

................... min .................. s  [3]

$\mathrm{f}\left(x\right)=8-3x$  and  $\mathrm{g}\left(x\right)=\frac{10}{x+1},x\ne -1$.

Write $\mathrm{f}\left(x\right)+\mathrm{g}\left(x\right)$ as a single fraction in its simplest form.

$2-\frac{x+2}{x-3}-\frac{x-6}{x+3}$ can be written as a single fraction in the form  $\frac{ax+b}{x^2-9}$ where a and b are integers.

Work out the value of a and the value of b.

Show that  $\frac{1}{6x^2+7x-5}÷\frac{1}{4x^2-1}$  simplifies to  $\frac{ax+b}{cx+d}$ where a, b, c and d are integers.