Question

Solve for x:
$\frac{1}{ a + b + x} = \frac{1}{a} + \frac{1}{b} + \frac{1}{x}$
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Answer 1

Step-by-step explanation:

1 / a+b+x = 1/ a + 1/b + 1/x

so,

1 /a+b+x - 1/x = a+b / ab

(x - a - b - x) / x(a+b+x) = a+b / ab

-(a+b) / x(a+b+x) = a+b /ab

- ab = ax + bx + x²

x² + ax + bx + ab = 0

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

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

so , x= a,b