Question

solve 5/x-2 - 3/x+6 =4/x using factorisation​

Answer 1

Step-by-step explanation:

We have

$\frac{5}{x - 2} - \frac{3}{x + 6} = \frac{4}{x} = \\ = > \frac{5(x + 6) - 3(x - 2)}{(x - 2)(x + 6)} = \frac{4}{x} \\ = > \frac{5x + 30 - 3x + 6}{ {x}^{2} + 6x - 2x - 12} = \frac{4}{x} \\ = > \frac{2x + 36}{ {x}^{2} + 4x - 12 } = \frac{4}{x} \\ = > x(2x + 36) = 4( {x}^{2} + 4x - 12) \\ = > 2 {x}^{2} + 36x = 4 {x}^{2} + 16x - 48 \\ = > - 2 {x}^{2} + 20x + 48 = 0 \\ = > {x}^{2} - 10x - 24 = 0 \\ = > {x}^{2} - (12 - 2)x - 24 = 0 \\ = > {x}^{2} - 12x + 2x - 24 = 0 \\ = > x(x - 12) + 2(x - 12) = 0 \\ = > (x - 12)(x + 2) = 0 \\ = > x - 12 = 0 \: \: or \: \: x + 2 = 0 \\ = > x = 12 \: \: or \: \: x = - 2$