Question

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

Answer 1

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

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

$\frac{a-a-b-x}{b+a+x}=\frac{x+b}{bx}$

$-(b+x)\left(bx\right)=(x+b)(a+b+x)$

$-bx=a+b+x$

$x(1+b)=-(a+b)$

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

Or $x=-b$