Question:
$\frac{8}{x}=\frac{5}{x-1}$
Solution:
Given, $\frac{8}{x}=\frac{5}{x-1}$'
$\Rightarrow$ $8(x-1)=5 x$ [by cross-multiplication]
$\Rightarrow \quad 8 x-8=5 x$
$\Rightarrow$ $8 x-5 x=8$ [transposing $5 x$ to LHS and $-8$ to RHS]
$\Rightarrow \quad 3 x=8$
$\Rightarrow$ $\frac{3 x}{3}=\frac{8}{3}$ [dividing both sides by 3 ]
$\therefore$ $x=\frac{8}{3}$