What is (x-5)/(x^4-2x^3)*(x^2-4)/(x^2-3x-10) ?

The solution to (x-5)/(x^4-2x^3)*(x^2-4)/(x^2-3x-10) is 1/(x^3)

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simplify (x-5)/(x^4-2x^3)*(x^2-4)/(x^2-3x-10)

simplify

\frac{x - 5}{x ^{4} - 2 x ^{3}} \cdot \frac{x ^{2} - 4}{x ^{2} - 3 x - 10}

\frac{1}{x ^{3}}

Solution steps

\frac{x - 5}{x ^{4} - 2 x ^{3}} \cdot \frac{x ^{2} - 4}{x ^{2} - 3 x - 10}

Cancel

\frac{x ^{2} - 4}{x ^{2} - 3 x - 10} : \frac{x - 2}{x - 5}

= \frac{x - 5}{x ^{4} - 2 x ^{3}} \cdot \frac{x - 2}{x - 5}

Cross-cancel common factor:

x - 5

= \frac{x - 2}{x ^{4} - 2 x ^{3}}

Factor

x^{4} - 2 x^{3} : x^{3} (x - 2)

= \frac{x - 2}{x ^{3} ( x - 2 )}

Cancel the common factor:

x - 2

= \frac{1}{x ^{3}}

(x - 5) (3 x + 1)

\frac{7 x}{6} - \frac{8 x}{6}

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

(n^{2} + 4) (n^{2} - 7)

(4 x - 1) (4 x + 1)

What is (x-5)/(x^4-2x^3)*(x^2-4)/(x^2-3x-10) ?
The solution to (x-5)/(x^4-2x^3)*(x^2-4)/(x^2-3x-10) is 1/(x^3)