which expression is equivalent to the following complex fraction?\n$\frac{\frac{2}{x}-\frac{4}{y}}{\frac{-5}{…

which expression is equivalent to the following complex fraction?\n$\frac{\frac{2}{x}-\frac{4}{y}}{\frac{-5}{y}+\frac{3}{x}}$\n$\frac{3y + 5x}{2(y - 2x)}$\n$\frac{2(y - 2x)}{3y - 5x}$\n$\frac{2(y - 2x)(3y - 5x)}{x^{2}y^{2}}$\n$\frac{x^{2}y^{2}}{2(y - 2x)(3y - 5x)}$

which expression is equivalent to the following complex fraction?\n$\frac{\frac{2}{x}-\frac{4}{y}}{\frac{-5}{y}+\frac{3}{x}}$\n$\frac{3y + 5x}{2(y - 2x)}$\n$\frac{2(y - 2x)}{3y - 5x}$\n$\frac{2(y - 2x)(3y - 5x)}{x^{2}y^{2}}$\n$\frac{x^{2}y^{2}}{2(y - 2x)(3y - 5x)}$

Answer

Explanation:

Step1: Simplify the numerator

Find a common - denominator for $\frac{2}{x}-\frac{4}{y}$. The common denominator of $x$ and $y$ is $xy$. So, $\frac{2}{x}-\frac{4}{y}=\frac{2y - 4x}{xy}=\frac{2(y - 2x)}{xy}$.

Step2: Simplify the denominator

Find a common - denominator for $\frac{-5}{y}+\frac{3}{x}$. The common denominator of $y$ and $x$ is $xy$. So, $\frac{-5}{y}+\frac{3}{x}=\frac{-5x + 3y}{xy}=\frac{3y-5x}{xy}$.

Step3: Divide the numerator by the denominator

The complex fraction $\frac{\frac{2}{x}-\frac{4}{y}}{\frac{-5}{y}+\frac{3}{x}}$ is equivalent to $\frac{\frac{2(y - 2x)}{xy}}{\frac{3y - 5x}{xy}}$. When dividing by a fraction, we multiply by its reciprocal, so $\frac{2(y - 2x)}{xy}\times\frac{xy}{3y - 5x}=\frac{2(y - 2x)}{3y - 5x}$.

Answer:

$\frac{2(y - 2x)}{3y - 5x}$