Question

Which expression is equivalent to the following complex fraction?

Answer 1

Answer:

B

Step-by-step explanation:

Simplify the numerator and denominator of the fraction, that is

$\frac{2}{x}$ - $\frac{4}{y}$

Multiply the numerator/denominator of the first fraction by y

Multiply the numerator/denominator of the second fraction by x

$\frac{2y}{xy}$ - $\frac{4x}{xy}$

= $\frac{2y-4x}{xy}$

Similarly

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

Multiply numerator/denominator of the first fraction by x

Multiply numerator/denominator of second fraction by y

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

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

To perform the division

leave the fraction on the numerator

Change division to multiplication

Turn the fraction on the denominator upside down, thus

$\frac{2y-4x}{xy}$ × $\frac{xy}{3y-5x}$

Cancel xy on the numerator and denominator

= $\frac{2y-4x}{3y-5x}$ ← factor 2 out of each term on the numerator

= $\frac{2(y-2x)}{3y-5x}$ → B