Question

Which expression is equivalent to the following complex fraction?

StartFraction 1 Over x EndFraction minus StartFraction 1 Over y EndFraction divided by StartFraction 1 Over x EndFraction + StartFraction 1 Over y EndFraction
StartFraction y + x Over y minus x EndFraction
StartFraction (y minus x) (y + x) Over x squared y squared EndFraction
StartFraction x squared y squared Over (y + x) (y + x) EndFraction
StartFraction y minus x Over y + x EndFraction

Answer 1

(1/x - 1/y) = (y - x)/(xy) and (1/x + 1/y) = (y + x)/(xy). Dividing gives [(y - x)/(xy)] / [(y + x)/(xy)] = (y - x)/(y + x).

Answer: (y - x)/(y + x).