Algebraic Fractions (Cambridge International IGCSE Mathematics): Exam Questions

Simplify.

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

Simplify.

$\frac{5}{3x}\times\frac{9x}{20}$

Simplify.

$\frac{x^{2}+5x}{x^{2}-25}$

Write as a single fraction in its simplest form.

$\frac{x-5}{3}+\frac{6}{x+2}$

Simplify $\frac{x^{2}-25}{x^{2}-2x-35}$.

Write $\frac{x-8}{x}+\frac{3x}{x+1}$ as a single fraction in its simplest form.

Simplify.

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

Simplify $\frac{x^{2}-25}{x^{2}-17x+60}$.

$\mathrm{f} ( x ) = 7 x - 4$ and $\mathrm{g} ( x ) = \frac{2 x}{x - 3} , x \text{eq} 3$

Find $\frac{ \mathrm{f} ( x ) }{2} + \mathrm{g} ( x )$. 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 $x$ = ..........................

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

Write $g(x)-f(x)$ as a single fraction in its simplest form.

Simplify.

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

Simplify.

$\frac{3y^{2}+18y}{4y^{2}-144}$

Solve.

$\frac{4x}{5x-1}=\frac{8}{7}$

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

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.

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]

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

Write $f(x)+g(x)$ 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 $\frac{1}{6x^{2}+7x-5}\div\frac{1}{4x^{2}-1}$ simplifies to $\frac{ax+b}{cx+d}$ where a, b, c and d are integers.