Solve equation using factorisation method: 3 x-2 2 x-3 =3 x-8 x+4 - Vidyadip

Question

Solve equation using factorisation method:
$\frac{3 x-2}{2 x-3}=\frac{3 x-8}{x+4}$

✓

Answer

$\frac{3 x-2}{2 x-3}=\frac{3 x-8}{x+4}$
$\Rightarrow(3 x-2)(x+4)=(2 x-3)(3 x-8) $
$\Rightarrow 3 x_2+12 x-2 x-8=6 x^2-16 x-9 x+24 $
$ \Rightarrow 3 x^2+10 x-8=6 x^2-25 x+24$
$\Rightarrow 3 x^2-35 x+32=0 $
$ \Rightarrow 3 x^2-32 x-3 x+32=0 $
$ \Rightarrow x(3 x-32)-1(3 x-32)=0 $
$ \Rightarrow(x-1)(3 x-32)=0$
If $x -1 = 0$ or $3x - 32 = 0$
$\Rightarrow x =1$ or $x =\frac{32}{3}=\frac{102}{3}$

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