# Test: Algebraic Fractions - Challenging

Double click on maths expressions to zoom
Question 1:   Simplify: $\frac{x-3}{y+1}\cdot \frac{y+1}{x-5}$
$1$
$\frac{x}{x-2}$
$\frac{x-5}{x-3}$
$\frac{x-3}{x-5}$
Question 2:   Simplify: $\frac{{x}^{4}-16}{{x}^{2}+4}$
${x}^{2}+4$
${x}^{2}-12$
${x}^{2}-4$
$x-2$
Question 3:   Simplify: $\frac{{x}^{2}-7x+12}{\left(x-3\right)\left(x+1\right)}$
$x-3$
$\frac{x-3}{x+1}$
$\frac{x-4}{x+1}$
$\frac{x+1}{x-4}$
Question 4:   Simplify: $\frac{8{\left(-x\right)}^{12}}{{x}^{9}}$
$-\frac{8}{{x}^{3}}$
$\frac{8}{{x}^{3}}$
$8{x}^{3}$
$-8{x}^{3}$
Question 5:   Simplify: $\frac{{x}^{3}-x}{1-x}$
$\frac{{x}^{2}-1}{x}$
$-{x}^{2}-1$
$-x\left(x+1\right)$
${x}^{2}-x$
Question 6:   Simplify: $\frac{3{x}^{2}-9x}{3-x}$
$3x$
$-x+3$
$x-3$
$-3x$
Question 7:   Simplify: $\frac{2{a}^{2}+8a}{{a}^{2}-16}$
$\frac{1}{a-2}$
$\frac{2}{a+2}$
$\frac{2a}{a-4}$
$\frac{4}{a+4}$
Question 8:   Simplify: $\frac{3}{x}:\frac{x-1}{x+1}\cdot \frac{x}{3}$
$\frac{x-1}{x+1}$
$\frac{x+1}{x-1}$
$-\frac{x+1}{x-1}$
$x$
Question 9:   Simplify:$\frac{2}{{x}^{2}}+\frac{x}{x+1}$
 $\frac{{x}^{3}+2x+2}{{x}^{2}\left(x+1\right)}$
$\frac{{x}^{3}+2{x}^{2}+x+1}{{x}^{2}+x+1}$
$\frac{{x}^{3}+2{x}^{2}+1}{{x}^{2}\left(x+1\right)}$
$\frac{2+x}{{x}^{2}+x+1}$
Question 10:   Simplify: $\frac{{x}^{2}+2x+1}{x+1}+\frac{{x}^{2}+x-2}{x+2}$
$\frac{2{x}^{2}+3x-1}{\left(x+1\right)\left(x+2\right)}$
$\frac{4{x}^{2}+3{x}^{2}+x-1}{\left(x+1\right)\left(x+2\right)}$
$\frac{2{x}^{3}+6{x}^{2}+4x}{\left(x+1\right)\left(x+2\right)}$
$\frac{3{x}^{3}+5{x}^{2}+3x}{\left(x+1\right)\left(x+2\right)}$