Question

Simplify:
$\frac{3}{2x^2+x-1}- \frac{2}{3x^2+2x-1}$.
Please answer quickly.

Answer 1

⇒$\frac{3}{2 x^{2}+x-1 } - \frac{2}{3 x^{2}+2x-1x }$

On taking the L.C.M we get ,
⇒$\frac{3(3 x^{2}+2x-1) -2(2 x^{2}+x-1) }{(2 x^{2}+2x-1)(3 x^{2}+2x-1) }$

⇒  $\frac{5 x^{2}+4x -1 }{(x+1)(2x-1)(3x-1)(x-1)}$

⇒$\frac{(x+1)(5x-1)}{(2x-1)(3x+1)(x-1)}$


Therefore ,
⇒$\frac{(x+1)(5x-1)}{(2x-1)(3x+1)(x+1)}$ 
is the required answer.

Answer 2

$\frac{3}{(2x-1)(x+1)}-\frac{2}{(3x-1)(x+1)}\\\\=\frac{3(3x-1)-2(2x-1)}{(2x-1)(3x-1)(x+1)}\\\\=\frac{5x-1}{(2x-1)(3x-1)(x+1)}$