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What is the difference? startfraction 2 x 5 over x squared minus 3 x endfraction minus startfraction 3 x 5 over x cubed minus 9 x endfraction minus startfraction x 1 over x squared minus 9 endfraction startfraction (x 5) (x 2) over x cubed minus 9 x endfraction startfraction (x 5) (x 4) over x cubed minus 9 x endfraction startfraction negative 2 x 11 over x cubed minus 12 x minus 9 endfraction startfraction 3 (x 2) over x squared minus 3 x endfraction

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MrRoyalidn

The difference of the expression [tex]\frac{2x^5}{x^2 - 3x} - \frac{3x^5}{x^3 - 9x}[/tex] is [tex]\frac{2x^5(x + 3) - 3x^5}{x(x - 3)(x + 3)}[/tex]

How to determine the difference?

The expression is given as:

[tex]\frac{2x^5}{x^2 - 3x} - \frac{3x^5}{x^3 - 9x}[/tex]

Factor the denominators of the expressions:

[tex]\frac{2x^5}{x(x - 3)} - \frac{3x^5}{x(x^2 - 9)}[/tex]

Apply the difference of two squares to x² - 9

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

Take LCM

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

Hence, the difference of the expression [tex]\frac{2x^5}{x^2 - 3x} - \frac{3x^5}{x^3 - 9x}[/tex] is [tex]\frac{2x^5(x + 3) - 3x^5}{x(x - 3)(x + 3)}[/tex]

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Answer:

A

Step-by-step explanation:

on Edge 2022

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