Question

1/x + 1/a=1/b,then x=

Answer 1

$\dfrac{1}{x}+\dfrac{1}{a}=\dfrac{1}{b}\ \ \ |subtract\ \dfrac{1}{a}\ from\ both\ sides\\\\\dfrac{1}{x}=\dfrac{1}{b}-\dfrac{1}{a}\\\\\dfrac{1}{x}=\dfrac{a}{ab}-\dfrac{b}{ab}\\\\\dfrac{1}{x}=\dfrac{a-b}{ab}\Rightarrow\dfrac{x}{1}=\dfrac{ab}{a-b}\to\boxed{x=\dfrac{ab}{a-b}}$