Question

1÷a+b+x=1÷a+1÷b+1÷x find the(roots of the question)solution of this question ​

Answer 1

$\frac{1}{a + b + x} = \frac{1}{a} + \frac{1}{b} + \frac{1}{x} \\ \frac{1}{a + b + x} - \frac{1}{x} = \frac{a + b}{ab} \\ \frac{x - a - b - x}{ {x}^{2} + (a + b)x} = \frac{a + b}{ab} \\ \frac{ - (a + b)}{ {x}^{2} + (a + b)x} = \frac{(a + b)}{ab} \\ - ab = {x}^{2} + (a + b)x \\ {x}^{2} + ax + bx + ab = 0 \\ x(x + a) + b(x + a) = 0 \\ (x + a)(x + b) = 0$

x + a = 0 or x + b = 0

x = -a or x = -b

Hence, x = -a or x = -b are the roots of the given equation.