which expression is equivalent to the following complex fraction?\n$\frac{\frac{-2}{x}+\frac{5}{y}}{\frac{3}{…

which expression is equivalent to the following complex fraction?\n$\frac{\frac{-2}{x}+\frac{5}{y}}{\frac{3}{y}-\frac{2}{x}}$\n$\frac{-2y + 5x}{3x - 2y}$\n$\frac{3x - 2y}{-2y + 5x}$\n$\frac{x^{2}y^{2}}{(-2y + 5x)(3x - 2y)}$\n$\frac{(-2y + 5x)(3x - 2y)}{x^{2}y^{2}}$

which expression is equivalent to the following complex fraction?\n$\frac{\frac{-2}{x}+\frac{5}{y}}{\frac{3}{y}-\frac{2}{x}}$\n$\frac{-2y + 5x}{3x - 2y}$\n$\frac{3x - 2y}{-2y + 5x}$\n$\frac{x^{2}y^{2}}{(-2y + 5x)(3x - 2y)}$\n$\frac{(-2y + 5x)(3x - 2y)}{x^{2}y^{2}}$

Answer

Explanation:

Step1: Combine numerator terms

Find a common - denominator for the numerator $\frac{-2}{x}+\frac{5}{y}$. The common denominator of $x$ and $y$ is $xy$. So, $\frac{-2}{x}+\frac{5}{y}=\frac{-2y + 5x}{xy}$.

Step2: Combine denominator terms

Find a common - denominator for the denominator $\frac{3}{y}-\frac{2}{x}$. The common denominator of $y$ and $x$ is $xy$. So, $\frac{3}{y}-\frac{2}{x}=\frac{3x-2y}{xy}$.

Step3: Rewrite the complex fraction

The original complex fraction $\frac{\frac{-2}{x}+\frac{5}{y}}{\frac{3}{y}-\frac{2}{x}}$ can be rewritten as $\frac{\frac{-2y + 5x}{xy}}{\frac{3x-2y}{xy}}$.

Step4: Simplify the complex fraction

When dividing by a fraction, we multiply by its reciprocal. So, $\frac{\frac{-2y + 5x}{xy}}{\frac{3x-2y}{xy}}=\frac{-2y + 5x}{xy}\times\frac{xy}{3x-2y}=\frac{-2y + 5x}{3x-2y}$.

Answer:

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