Question

solve this,,,,,,,,,,,,,,,,,,,

Answer 1

$\underline\bold{\huge{SOLUTION \: :}}$

$\bold{CORRECT\:\:QUESTION}$

$\frac{1}{a + b + x} = \frac{1}{a} + \frac{1}{b} + \frac{1}{x}$

=> $\frac{1}{a + b + x} - \frac{1}{x} = \frac{1}{a} + \frac{1}{b}$

=> $\frac{x - a - b - x}{x(a + b + x)} = \frac{b + a}{ab}$

=> $\frac{ - (a + b)}{ax + bx + {x}^{2} } = \frac{a + b}{ab}$

=> $\frac{ - 1}{ {x}^{2} + ax + bx } = \frac{1}{ab}$

=> ${x}^{2} + ax + bx = - ab$

=> ${x}^{2} + ax + bx + ab = 0$

=> $x(x + a) + b(x + a) = 0$

______________________________

$\bold{EITHER :}$

$x+ a = 0$

=> $x = - a$

______________________________

$\bold{OR :}$

$x + b = 0$

$x = - b$

$\bold{THUS\:\:THE\:\: SOLUTION\:\:IS\:\:x = -a, -b}$