What is (\frac{x^3)/(x^2-4)}{(2x)/(x^2-7x+10)} ?

The solution to (\frac{x^3)/(x^2-4)}{(2x)/(x^2-7x+10)} is (x^2(x-5))/(2(x+2))

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simplify (\frac{x^3)/(x^2-4)}{(2x)/(x^2-7x+10)}

simplify

\frac{\frac{x ^{3}}{x ^{2} - 4}}{\frac{2 x}{x ^{2} - 7 x + 10}}

\frac{x ^{2} ( x - 5 )}{2 ( x + 2 )}

Solution steps

\frac{\frac{x ^{3}}{x ^{2} - 4}}{\frac{2 x}{x ^{2} - 7 x + 10}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{x ^{3} ( x ^{2} - 7 x + 10 )}{( x ^{2} - 4 ) \cdot 2 x}

Cancel

\frac{x ^{3} ( x ^{2} - 7 x + 10 )}{( x ^{2} - 4 ) \cdot 2 x} : \frac{x ^{2} ( x - 5 )}{( x + 2 ) \cdot 2}

= \frac{x ^{2} ( x - 5 )}{( x + 2 ) \cdot 2}

= \frac{x ^{2} ( x - 5 )}{2 ( x + 2 )}

(3 x + 1) (2 x^{2} - 9 x + 5)

1 - 12

2 \cdot (- 8)

(1 + i) (2 + 3 i) (4 - 3 i)

\frac{14}{30}

What is (\frac{x^3)/(x^2-4)}{(2x)/(x^2-7x+10)} ?
The solution to (\frac{x^3)/(x^2-4)}{(2x)/(x^2-7x+10)} is (x^2(x-5))/(2(x+2))