Question
if $a : b =5: 3$ find $\frac{5 a-3 b}{5 a+3 b}$
✓
Answer
$a : b = 5 : 3$
$\Rightarrow \frac{a}{b}=\frac{5}{3}$
$\frac{5 a-3 b}{5 a+3 b}=\frac{5\left(\frac{a}{b}\right)-3}{5\left(\frac{a}{b}\right)+3} ($ Dividing each term by $3)$
$=\frac{5\left(\frac{5}{3}\right)-3}{5\left(\frac{5}{3}\right)+\{3)}$
$=\frac{\frac{25}{3}-3}{\frac{25}{3}+3}$
$=\frac{25-9}{25+9}$
$=\frac{16}{34}=\frac{8}{17}$
$\Rightarrow \frac{a}{b}=\frac{5}{3}$
$\frac{5 a-3 b}{5 a+3 b}=\frac{5\left(\frac{a}{b}\right)-3}{5\left(\frac{a}{b}\right)+3} ($ Dividing each term by $3)$
$=\frac{5\left(\frac{5}{3}\right)-3}{5\left(\frac{5}{3}\right)+\{3)}$
$=\frac{\frac{25}{3}-3}{\frac{25}{3}+3}$
$=\frac{25-9}{25+9}$
$=\frac{16}{34}=\frac{8}{17}$
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