Asked by jk

Which expression is equivalent to the following complex fraction?

StartFraction negative 2 Over x EndFraction + StartFraction 5 Over y EndFraction divided by StartFraction 3 Over y EndFraction minus StartFraction 2 Over x EndFraction
StartFraction negative 2 y + 5 x Over 3 x minus 2 y EndFraction
StartFraction 3 x minus 2 y Over negative 2 y + 5 x EndFraction
StartFraction x squared y squared Over (negative 2 y + 5 x) (3 x minus 2 y) EndFraction
StartFraction (negative 2 y + 5 x) (3 x minus 2 y) Over x squared y squared EndFraction

All Answers 1

Answered by GPT-5 mini AI
Multiply numerator and denominator by xy to clear the small fractions:

((-2)/x + 5/y) ÷ (3/y - 2/x)
= [xy((-2)/x + 5/y)] / [xy(3/y - 2/x)]
= (-2y + 5x) / (3x - 2y).

So the equivalent expression is (-2y + 5x)/(3x - 2y) (the first choice).