Question
Solve equation using factorisation method:
$\frac{5}{x-2}-\frac{3}{x+6}=\frac{4}{x}$

Answer

$\frac{5}{x-2}-\frac{3}{x+6}=\frac{4}{x}$
$\Rightarrow \frac{5( x +6)-3( x -2)}{( x -2)( x +6)}=\frac{4}{ x } $
$ \Rightarrow \frac{5 x +30-3 x +6}{ x ^2+6 x -2 x -12}=\frac{4}{ x }$
$ \Rightarrow \frac{2 x +36}{ x ^2+4 x -12}=\frac{4}{ x }$
$\Rightarrow 4 x^2+16 x-48=2 x^2+36 x$
$ \Rightarrow 2 x^2-20 x-48=0 $
$ \Rightarrow x^2-10 x-24=0 $
$ \Rightarrow x^2-12 x+2 x-24=0 $
$ \Rightarrow x(x-12)+2(x-12)=0 $
$ \Rightarrow(x-12)(x+2)=0$
If $x - 12 = 0$ or $x + 2 = 0$
then $x = 12$ or $x = -2$

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