Question

2/x+1 + 4/x-2 = 9/18x+12​

Answer 1

I have done upto this...

U can refer to this attachment

Answer 2

Step-by-step explanation:

The given equation is

$\frac{2}{x + 1} + \frac{4}{x - 2} = \frac{9}{18x + 12}$

$or \: 2( \frac{1(x - 2) + 2(x + 1)}{(x + 1)(x - 2)} ) = \frac{9}{6(3x + 2)}$

$or \: \frac{2(x - 2 + 2x + 2)}{ {x}^{2} - 2x + x - 2 } = \frac{3}{2(3x + 2)}$

$or \: \frac{6x}{ {x}^{2} - x - 2 } = \frac{3}{2(3x + 2)}$

$or \: {x}^{2} - x - 2 = 4x(3x + 2)$

$or \: {x}^{2} - x - 2 = 12 {x}^{2} + 8x$

$or \: 12 {x}^{2} - {x}^{2} + 8x + x + 2 = 0$

$or \: 11 {x}^{2} + 9x + 2 = 0$

$therefore \: x = \frac{ - 9 + \sqrt{ {9}^{2} - 4 \times 11 \times 2} }{2 \times 11} or \frac{ - 9 - \sqrt{ {9}^{2} - 4 \times 11 \times 2} }{2 \times 11}$

$or \: \frac{ - 9 + \sqrt{ - 7} }{22} and \frac{ - 9 - \sqrt{ - 7} }{22}$