Question

Solve for x -


`(1)/(a) + (1)/(b) + (1)/(x) = (1)/(a + b + x)`
80 points !!! Pls help

Answer 1

`QUADRATIC \: \: RESOLUTIONS \\ \\ \\ Given \: \:expression - \\ \\ (1)/(a) + (1)/(b) + (1)/(c) = (1)/(a + b + x) \\ \\ (1)/(a) + (1)/(b) = (1)/(a + b + x) - (1)/(x) \\ \\ (a + b)/(ab) = ( - (a + b))/(x(a + b + x)) \\ \\ (1)/(ab) = ( - 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.`

Answer 2

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