Which expression is equivalent to the following complex fraction?SIMI3+3y+5x2(y-2x)2(y-2x)3y-5xo122(y-2x)(3y-5x)x²,2x²y²2(y-2x) (3y-5x

Question

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$Which expression is equivalent to the following complex fractionSIMI33y5x2y2x2y2x3y5xo122y2x3y5xx2xy2y2x 3y5x class=$

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TallieV707715 TallieV707715 · Answer 1 · 2022-10-25T21:17:21+02:00

Solution

For this case we can do the following:

[tex]\frac{\frac{2}{x}-\frac{4}{y}}{-\frac{5}{y}+\frac{3}{x}}[/tex]

We can start with the numerator and we have:

[tex]\frac{2}{x}-\frac{4}{y}=\frac{2y-4x}{xy}=\frac{2(y-2x)}{xy}[/tex]

For the denominator we have:

[tex]-\frac{5}{y}+\frac{3}{x}=\frac{3y-5x}{xy}[/tex]

And replacing we got:

[tex]\frac{\frac{2(y-2x)}{xy}}{\frac{3y-5x}{xy}}=\frac{2(y-2x)}{3y-5x}[/tex]

Then the correct answer would be:

[tex]\frac{2(y-2x)}{3y-5x}[/tex]