SOLUTION: Given (1/x) = (1/a) + (1/b), 1. Solve to show x = ab/(a + b), provided that a + b does no equal 0. 2. Check the solution.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Given (1/x) = (1/a) + (1/b), 1. Solve to show x = ab/(a + b), provided that a + b does no equal 0. 2. Check the solution.       Log On


   

Question 1207838: Given (1/x) = (1/a) + (1/b),
1. Solve to show x = ab/(a + b), provided that a + b does no equal 0.
2. Check the solution.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Not much outside of just the algebra steps solving for one variable in an equation.

1%2Fx=%281%2Fa%2B1%2Fb%29

on right side, simplest common denominator ab.

1%2Fx=b%2F%28ab%29%2Ba%2F%28ab%29

1%2Fx=%28b%2Ba%29%2F%28ab%29

and just recognize, the reciprocal of each side is what you are looking for.

x=%28ab%29%2F%28b%2Ba%29

x=%28ab%29%2F%28a%2Bb%29----------result.

Obviously if a=-b then, not allowed for a equal to negative b.