Question

1/ x-3 + 2/ x-2 = 8/x. Please friends help me solve this :-)

Answer 1

$\frac{1}{x - 3} + \frac{2}{x - 2} = \frac{8}{x} \\ \frac{(x -2) +2(x - 3) }{ (x - 3)(x - 2)} = \frac{8}{x} \\ \frac{3x - 8}{x {}^{2} - 5x + 6} = \frac{8}{x} \\ \frac{3x {}^{2} - 8x}{x {}^{2} - 5x + 6 } = 8 \\ 3x {}^{2} - 8x = 8x {}^{2} - 40x + 6 \times 8 \\ 8x {}^{2 } - 3x {}^{2} - 40x + 8x + 48 = 0 \\ 5x {}^{2} - 32x + 48 = 0$

5x²-20x-12x+48=0
5x(x-4)-12(x-4)=0
(5x-12)(x-4)=0
x=12/5,4

Answer 2

1/x-3 + 2/x-2 = 8/x.
Taking LCM.

{x-2+ 2(x-3)}/(x-3)(x-2)= 8/x.

x-2+2x-6/x^2-2x-3x-6= 8/x.

3x-8/x^2-5x-6=8/x.

Cross multiplication.

3x^2-8x=8x^2 -40x+48.

8x^2-3x^2-40x+8x+48=0.

5x^2 -32x +48=0.

5x^2 -20x-12x+48=0.

5x(x-4)-12(x-4)=0.

(5x-12)(x-4)=0.

Hope it helps.