Equivalent expressions are expressions that have equal values
The equivalent of the complex fraction is [tex]\frac{5x-2y}{3x - 2y}[/tex]
The complex fraction is given as:
[tex](-\frac{2}{x}+ \frac{5}{y}) \div (\frac{3}{y} - \frac{2}{x})[/tex]
Start by taking the LCMs of the expressions in the brackets
[tex](-\frac{2}{x}+ \frac{5}{y}) \div (\frac{3}{y} - \frac{2}{x}) = \frac{-2y + 5x}{xy} \div \frac{3x - 2y}{xy}[/tex]
Rewrite the fraction as follows:
[tex](-\frac{2}{x}+ \frac{5}{y}) \div (\frac{3}{y} - \frac{2}{x}) = \frac{5x-2y}{xy} \div \frac{3x - 2y}{xy}[/tex]
Express the division as a product
[tex](-\frac{2}{x}+ \frac{5}{y}) \div (\frac{3}{y} - \frac{2}{x}) = \frac{5x-2y}{xy} \times \frac{xy}{3x - 2y}[/tex]
Cancel out common factors
[tex](-\frac{2}{x}+ \frac{5}{y}) \div (\frac{3}{y} - \frac{2}{x}) = \frac{5x-2y}{1} \times \frac{1}{3x - 2y}[/tex]
Rewrite as:
[tex](-\frac{2}{x}+ \frac{5}{y}) \div (\frac{3}{y} - \frac{2}{x}) = \frac{5x-2y}{3x - 2y}[/tex]
Hence, the equivalent of the complex fraction is [tex]\frac{5x-2y}{3x - 2y}[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/15715866
