The equivalent expression of [tex]\frac{\frac 2x - \frac 4y}{-\frac 5y + \frac 3x}[/tex] is [tex]\frac {2(y - 2x)}{ 3y-5x}[/tex]
How to determine the equivalent expression?
The complete question is in the attached image
We have:
[tex]\frac{\frac 2x - \frac 4y}{-\frac 5y + \frac 3x}[/tex]
Take the LCM
[tex]\frac{\frac {2y - 4x}{xy}}{\frac{-5x + 3y}{xy}}[/tex]
Divide through by xy
[tex]\frac {2y - 4x}{-5x + 3y}[/tex]
Rewrite as:
[tex]\frac {2y - 4x}{ 3y-5x}[/tex]
Factor out 2
[tex]\frac {2(y - 2x)}{ 3y-5x}[/tex]
Hence, the equivalent expression of [tex]\frac{\frac 2x - \frac 4y}{-\frac 5y + \frac 3x}[/tex] is [tex]\frac {2(y - 2x)}{ 3y-5x}[/tex]
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