3 months ago

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

Mathematics

1 answer:

lawyer [12.5K]3 months ago

6 0

Answer:

The equivalent expression for the provided complex fraction is

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

Step-by-step explanation:

To simplify the complex fraction, calculating the numerator and denominator individually is effective.

Numerator:

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

Denominator:

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

Resolving 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 will cancel out (Cross multiplication):

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

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