Question

solve the equation bye factorisation method​

Answer 1

$\fbox{Solution\:of\:(i)}$

$\frac{8}{x + 3} - \frac{3}{2 - x} = 2 \\ = > \frac{8 - 3}{(x + 3) - (2 - x)} = 2 \\ = > \frac{5}{x + 3 - 2 + x} = 2 \\ = > \frac{5}{2x + 1} = 2 \\ = > 5 = 2(2x + 1) \\ = > 4x + 2 = 5 \\ = > 4x = 5 - 2 \\ = > 4x = 3 \\ = > x = \frac{3}{4} \\ = > x = 0.75$

$\fbox{Solution\:of\:(ii)}$

$\frac{x + 1}{x - 1} + \frac{x - 2}{x + 2} = 3 \\ = > \frac{(x + 1) + (x - 2)}{(x - 1) + (x - 2)} = 3 \\ = > \frac{x + 1 + x - 2}{x - 1 + x - 2} = 3 \\ = > \frac{2x - 1}{2x - 3} = 3 \\ = > 2x - 1 = 3(2x - 3) \\ = > 2x - 1 = 6x - 3 \\ = > 2x - 6x = - 3 + 1 \\ = > - 4x = - 2 \\ = > x = \frac{ - 2}{ - 4} \\ = > x = \frac{1}{2} \\ = > x = 0.5$