Question

If $a:b=5:3$, find: $\frac{5a-3b}{5a+3b}$

Answer 1

Find the value of $\frac{5a-3b}{5a+3b}$

Given: $a:b=5:3$
$\Rightarrow \frac{a}{b}=\frac{5}{3}\dots \left[1\right]$

To find : $\frac{5a-3b}{5a+3b}$

Divide the numerator and denominator both by $"b"$
$\frac{5a-3b}{5a+3b}=\frac{5\left(\frac{a}{b}\right)-3}{5\left(\frac{a}{b}\right)+3}$
$=\frac{5\times \left(\frac{5}{3}\right)-3}{5\times \left(\frac{5}{3}\right)+3}$ [From$\left(1\right)$]
$=\frac{\frac{25-9}{3}}{\frac{25+9}{3}}$
$=\frac{25-9}{25+9}$
$=\frac{16}{34}$
$=\frac{8}{17}$

Hence the value of $\frac{5a-3b}{5a+3b}$ is $\frac{8}{17}$.