Question

Solve for x -

Answer 1

Too much to write ... so I have hand written the answer. 

Answer 2

$QUADRATIC \: \: RESOLUTIONS \\ \\ \\ Given \: \:expression - \\ \\ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{1}{a + b + x} \\ \\ \frac{1}{a} + \frac{1}{b} = \frac{1}{a + b + x} - \frac{1}{x} \\ \\ \frac{a + b}{ab} = \frac{ - (a + b)}{x(a + b + x)} \\ \\ \frac{1}{ab} = \frac{ - 1}{x(a + b + x)} \\ \\ Simplifying \: \: above \: \: expression \: \: , \: \\ \\ We \: get \: a \: Quadratic \: equation \: - \\ \\ {x}^{2} + (a + b)x + ab = 0 \\ \\ (x + a)(x + b) = 0 \\ \\ \\ || \: \: \: x = - a \: \: \: || \: \: \: x = - b \: \: \: || \: \: \: \: \: \: \: \: \: \: \: Ans.$