Solve the following

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)

$\Rightarrow 9 x^{2}-7 x+54 x-42=9 x^{2}-12 x+15 x-20$

$\Rightarrow 9 x^{2}+47 x-42=9 x^{2}+3 x-20$

$\Rightarrow 9 x^{2}-9 x^{2}+47 x-3 x=-20+42$

$\Rightarrow 44 x=22$

$\Rightarrow x=\frac{22}{44}=\frac{1}{2}$

$\therefore x=\frac{1}{2}$

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