# How do you solve (3x)/(x+1)=12/(x^2-1)+2?

Sep 23, 2017

Solution: $x = 5 , x = - 2$

#### Explanation:

$\frac{3 x}{x + 1} = \frac{12}{{x}^{2} - 1} + 2$ or

$\frac{3 x}{x + 1} - \frac{12}{{x}^{2} - 1} = 2$ Multiplying by $\left({x}^{2} - 1\right)$ on both

sides we get $3 x \left(x - 1\right) - 12 = 2 \left({x}^{2} - 1\right)$ or

$3 {x}^{2} - 3 x - 12 = 2 {x}^{2} - 2$ or

 x^2-3x = 10 or x^2 -3x +9/4 = 10 +9/4 ; (9/4) is added

on both side to make L.H.S a square.

${\left(x - \frac{3}{2}\right)}^{2} = \frac{49}{4} \mathmr{and} x - \frac{3}{2} = \pm \sqrt{\frac{49}{4}}$ or

$x - \frac{3}{2} = \pm \frac{7}{2} \therefore x = \frac{3}{2} \pm \frac{7}{2} \mathmr{and} x = \frac{1}{2} \left(3 \pm 7\right) \therefore$

$x = 5 , x = - 2$ . Solution: $x = 5 , x = - 2$ [Ans]