Question

solve for x :
$\frac{x - 2}{x - 4} + \frac{x - 6}{x - 11} = 6 \times \frac{2}{3}$
​x not equal to 4,8.

Answer 1

Step-by-step explanation:

$\frac{x - 2}{x - 4} + \frac{x - 6}{x - 11} = 6 \times \frac{2}{3}$

$\frac{x - 2}{x - 4} + \frac{x - 6}{x - 11} = 4$

$\frac{( x - 2)(x - 11) + (x - 4)(x - 6)}{(x - 4)(x - 11)} = 4$

$= \frac{ {x}^{2} - 11x - 2x - 22 + {x}^{2} - 4x - 6x - 24}{ {x}^{2} - 4x - 11x - 44}$

$\frac{2 {x}^{2} - 23x - 46}{ {x}^{2} - 15x - 44 } = 4$

$2 {x}^{2} - 23x - 46 = 4( {x}^{2} - 15x - 44)$

$2 {x}^{2} - 23x - 46 = 4 {x}^{2} - 60x - 176$

$2 {x}^{2} - 37x + 222 = 0$