Question

Solve this question please....the answer is 12,-2​

Answer 1

Answer :-

12 , -2

Given to find the value of x

$\dfrac{5}{x - 2} - \dfrac{3}{x + 6} = \dfrac{4}{x}$

SOLUTION:-

Take L.C.M to the denominators of L.H.S

$\dfrac{5(x + 6) - 3(x - 2)}{(x - 2)(x + 6)} = \dfrac{4}{x}$

Simplifying the L.H.S

$\dfrac{5x + 30 - 3x + 6}{x(x + 6) - 2(x + 6)} = \dfrac{4}{x}$

$\dfrac{5x - 3x + 30 + 6}{x {}^{2} + 6x - 2x - 12 } = \dfrac{4}{x}$

$\dfrac{2x + 36}{x {}^{2} + 4x - 12} = \dfrac{4}{x}$

Cross multiplication

$(2x + 36)x = 4( {x}^{2} + 4x - 12)$

$2 x{}^{2} + 36x = 4 {x}^{2} + 16x - 48$

Transpose all terms to L.H.S

$2x {}^{2} + 36x - 4x {}^{2} - 16x + 48$

Keep like terms together

$2x {}^{2} - 4x {}^{2} + 36x - 16x + 48 = 0$

$- 2x {}^{2} + 20x + 48 = 0$

Take common "2"

$2( - x {}^{2} + 10x + 24) = 0$

$- x {}^{2} + 10x + 24 = 0$

Take common " - "

$x {}^{2} - 10x - 24 = 0$

Splitting the middle term

$x {}^{2} - 12x + 2x - 24 = 0$

$x(x - 12) + 2(x - 12) = 0$

$(x - 12)(x + 2) = 0$

$x - 12 = 0 \\ x = 12$

$x + 2 = 0 \\ x = - 2$

So, the value of x is 12 , -2