Answer
$\frac{x+5}{7}\div\frac{4x+20}{9}$
$=\frac{x+5}{7}\times\frac{9}{4x+20}$
$=\frac{x+5}{7}\times\frac{9}{4(x+5)}$
$=\frac{1}{7}\times\frac{9}{4}$
$=\frac{9}{28}$
Work Step by Step
To divide rational expressions the first step is to invert the divisor and multiply. This is done by flipping the second fraction, $\frac{4x+20}{9}$ so that it becomes $\frac{9}{4x+20}$ and changing the division to multiplication. The next step is to factorise as many numerators and denominators as possible. In this case $4x+20$ can be factorised to $4(x+5)$ as the highest common multiple is $4$. The next step is to divide the common numerators and denominators so that they cancel out. $x+5$ is the only common numerator and denominator so they both cancel each other out. Because $x+5$ goes into $x+5$ once the numerator for the first fraction is $1$. The second fraction is left with a denominator of $4$. Lastly the two fractions are simplified to give the final answer.
