# How do you solve 1/(x-6) + 1/(x-2)= 6/5 ?

Oct 7, 2017

Solution : $x = 7 , x = \frac{8}{3}$

#### Explanation:

$\frac{1}{x - 6} + \frac{1}{x - 2} = \frac{6}{5}$. Multiplying by $5 \left(x - 6\right) \left(x - 2\right)$ on both

sides we get $5 \left(x - 2\right) + 5 \left(x - 6\right) = 6 \left(x - 6\right) \left(x - 2\right)$ or

$5 x - 10 + 5 x - 30 = 6 \left({x}^{2} - 8 x + 12\right)$or

$10 x - 40 = 6 {x}^{2} - 48 x + 72$ or

$6 {x}^{2} - 48 x + 72 - 10 x + 40 = 0 \mathmr{and} 6 {x}^{2} - 58 x + 112 = 0$ or

$3 {x}^{2} - 29 x + 56 = 0 \mathmr{and} 3 {x}^{2} - 21 x - 8 x + 56 = 0$ or

$3 x \left(x - 7\right) - 8 \left(x - 7\right) = 0 \mathmr{and} \left(x - 7\right) \left(3 x - 8\right) = 0$

$\therefore x = 7 , x = \frac{8}{3} \therefore$ Solution : $x = 7 , x = \frac{8}{3}$ [Ans]