Answer:
The expression equivalent to the given complex fraction is
[tex]\frac{-2x+5y}{3x-2y}[/tex]
Step-by-step explanation:
An easy way to solve the complex fraction is to solve the numerator and denominator separately.
Numerator:
[tex]\frac{-2}{x} + \frac{5}{y}\\ = \frac{-2y + 5x}{xy}[/tex]
Denominator:
[tex]\frac{3}{y} + \frac{-2}{x}\\ = \frac{3x - 2y}{xy}[/tex]
Solving the complex fraction:
[tex][\frac{-2}{x} + \frac{5}{y}] / [\frac{3}{y} + \frac{-2}{x}]\\= [\frac{-2y + 5x}{xy}] / [\frac{3x - 2y}{xy}][/tex]
[tex]=\frac{-2y + 5x}{xy} * \frac{xy}{3x - 2y}[/tex]
Common terms in the numerator and denominator cancels each other(Cross multiplication) :
[tex]= \frac{-2y + 5x}{3x - 2y}[/tex]
