Question

If a ≠ b and 1/x + 1/a = 1/b , then x =

Answer 1

combine LHS

\[\frac{a +x}{ax} = \frac{1}{b}\]
cross-multiply
\[ab + bx = ax\]
get "x" terms on same side, factor out the "x"
\[x(a-b) = ab\]
divide
\[x = \frac{ab}{a-b}\]