Question:
Solve;
$\frac{9 x-7}{3 x+5}=\frac{3 x-4}{x+6}$
Solution:
$\frac{9 x-7}{3 x+5}=\frac{3 x-4}{x+6}$
$\Rightarrow(x+6)(9 x-7)=(3 x+5)(3 x-4)$ (by cross multiplication)
$\Rightarrow 9 x^{2}-7 x+54 x-42=9 x^{2}-12 x+15 x-20$
$\Rightarrow 9 x^{2}+47 x-42=9 x^{2}+3 x-20$
$\Rightarrow 9 x^{2}-9 x^{2}+47 x-3 x=-20+42$
$\Rightarrow 44 x=22$
$\Rightarrow x=\frac{22}{44}=\frac{1}{2}$
$\therefore x=\frac{1}{2}$