Question

1/(x+2) (x+3)+1/(x+3) (x+4)=1/(x+2) (x+8). PLEASE SOLVE THIS EQUATION IMMEDIATELY. ​

Answer 1

$\frac{1}{(x + 2)(x + 3)} + \frac{1}{(x + 3)(x + 4)} = \frac{1}{(x + 2)(x + 8)} \\ = > \frac{x + 4 + x + 2}{(x + 2)(x + 4)(x + 3)} = \frac{1}{(x + 2)(x + 8) } \\ = > {x}^{2} + 4x + 3x + 12 = (2x + 6)(x + 8) \\ = > {x}^{2} + 7x + 12 = 2 {x}^{2} + 16x + 6x + 48 \\ = > { x}^{2} + 15x + 36 = 0 \\ = > {x}^{2} + 12x + 3x + 36 = 0 \\ = > x(x + 12) + 3(x + 12) = 0 \\ = > (x + 3)(x + 12) = 0 \\ = > x = - 3 \: or \: x = - 12$