Question

solve the quadratic equation 1 upon X + 1 + 2 upon X + 2 is equal to 5 upon X + 4​

Answer 1

$\frac{1}{x + 1} + \frac{2}{x + 2} = \frac{5}{x + 4} \\ \frac{(x + 2) + 2(x + 1)}{(x + 1)(x + 2)} = \frac{5}{x + 4} \\ \frac{x + 2 + 2x + 2}{ {x}^{2} + 3x + 2 } = \frac{5}{x + 4} \\ (3x + 4)(x + 4) = 5( {x}^{2} + 3x + 2) \\ 3 {x}^{2} + 16x + 16 = 5 {x}^{2} + 15x + 10 \\ 2{x}^{2} - x - 6 = 0 \\ 2 {x}^{2} - 4x + 3x - 6 = 0 \\ 2x(x - 2) + 3(x - 2) = 0 \\ (2x + 3)(x - 2) = 0 \\ \\ x = \frac{ - 3}{2} \: or\: 2$

there you go :)