Question

Solve for x:
$\frac{(x+1)}{(3x-7)}=\frac{(x-1)}{(2x-5)}$

Answer 1

$\frac{(x+1)}{(3x-7)}=\frac{(x-1)}{(2x-5)}$
Cross multiply and you get,
$\Rightarrow$ (x + 1)(2x-5)=(x-1) (3x-7)
$\Rightarrow$ $2x^2-5x+2x-5=3x^2-3x-7x+7$
$\Rightarrow$ $-x^2+7x-12=0$
$\Rightarrow$ $x^2-7x+12=0$
$\Rightarrow$ $x^2-4x-3x+12=0$
$\Rightarrow$ $x(x-4)-3(x-4)$
$\Rightarrow$ $(x-3)(x-4)=0$
$\Rightarrow$ $x=3orx=4$