Question

Which expression is equivalent to the following complex fraction? StartFraction 2 Over x EndFraction minus StartFraction 4 Over y EndFraction divided by StartFraction negative 5 Over y EndFraction + StartFraction 3 Over x EndFraction StartFraction 3 y + 5 x Over 2 (y minus 2 x) EndFraction StartFraction 2 (y minus 2 x) Over 3 y minus 5 x EndFraction StartFraction 2 (y minus 2 x) (3 y minus 5 x) Over x squared y squared EndFraction StartFraction x squared y squared Over 2 (y minus 2 x) (3 y minus 5 x) EndFraction

Answer 1

The equivalent expression of $\frac{\frac 2x - \frac 4y}{-\frac 5y + \frac 3x}$ is $\frac {2(y - 2x)}{ 3y-5x}$

How to determine the equivalent expression?

The complete question is in the attached image

We have:

$\frac{\frac 2x - \frac 4y}{-\frac 5y + \frac 3x}$

Take the LCM

$\frac{\frac {2y - 4x}{xy}}{\frac{-5x + 3y}{xy}}$

Divide through by xy

$\frac {2y - 4x}{-5x + 3y}$

Rewrite as:

$\frac {2y - 4x}{ 3y-5x}$

Factor out 2

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

Hence, the equivalent expression of $\frac{\frac 2x - \frac 4y}{-\frac 5y + \frac 3x}$ is $\frac {2(y - 2x)}{ 3y-5x}$

Read more about equivalent expression at:

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