Question

(Please Hurry!) Which expression is equivalent to the following complex fraction?

Answer 1

Answer:

The expression equivalent to the given complex fraction is

$\frac{-2x+5y}{3x-2y}$

Step-by-step explanation:

An easy way to solve the complex fraction is to solve the numerator and denominator separately.

Numerator:

$\frac{-2}{x} + \frac{5}{y}\\ = \frac{-2y + 5x}{xy}$

Denominator:

$\frac{3}{y} + \frac{-2}{x}\\ = \frac{3x - 2y}{xy}$

Solving the complex fraction:

$[\frac{-2}{x} + \frac{5}{y}] / [\frac{3}{y} + \frac{-2}{x}]\\= [\frac{-2y + 5x}{xy}] / [\frac{3x - 2y}{xy}]$

$=\frac{-2y + 5x}{xy} * \frac{xy}{3x - 2y}$

Common terms in the numerator and denominator cancels each other(Cross multiplication) :

$= \frac{-2y + 5x}{3x - 2y}$