Answer:
B
Step-by-step explanation:
Simplify the numerator and denominator of the fraction, that is
[tex]\frac{2}{x}[/tex] - [tex]\frac{4}{y}[/tex]
Multiply the numerator/denominator of the first fraction by y
Multiply the numerator/denominator of the second fraction by x
[tex]\frac{2y}{xy}[/tex] - [tex]\frac{4x}{xy}[/tex]
= [tex]\frac{2y-4x}{xy}[/tex]
Similarly
[tex]\frac{-5}{y}[/tex] + [tex]\frac{3}{x}[/tex]
Multiply numerator/denominator of the first fraction by x
Multiply numerator/denominator of second fraction by y
[tex]\frac{-5x}{xy}[/tex] + [tex]\frac{3y}{xy}[/tex]
= [tex]\frac{3y-5x}{xy}[/tex]
To perform the division
leave the fraction on the numerator
Change division to multiplication
Turn the fraction on the denominator upside down, thus
[tex]\frac{2y-4x}{xy}[/tex] × [tex]\frac{xy}{3y-5x}[/tex]
Cancel xy on the numerator and denominator
= [tex]\frac{2y-4x}{3y-5x}[/tex] ← factor 2 out of each term on the numerator
= [tex]\frac{2(y-2x)}{3y-5x}[/tex] → B
