What is (x^3-9x)/(x^2+10x+21)*(x^2+7x)/(x^2+5x-24) ?

The solution to (x^3-9x)/(x^2+10x+21)*(x^2+7x)/(x^2+5x-24) is (x^2)/(x+8)

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simplify (x^3-9x)/(x^2+10x+21)*(x^2+7x)/(x^2+5x-24)

simplify

\frac{x ^{3} - 9 x}{x ^{2} + 10 x + 21} \cdot \frac{x ^{2} + 7 x}{x ^{2} + 5 x - 24}

\frac{x ^{2}}{x + 8}

Solution steps

\frac{x ^{3} - 9 x}{x ^{2} + 10 x + 21} \cdot \frac{x ^{2} + 7 x}{x ^{2} + 5 x - 24}

Cancel

\frac{x ^{3} - 9 x}{x ^{2} + 10 x + 21} : \frac{x ( x - 3 )}{x + 7}

= \frac{x ( x - 3 )}{x + 7} \cdot \frac{x ^{2} + 7 x}{x ^{2} + 5 x - 24}

Apply the fraction rule:

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

= \frac{x ( x - 3 ) ( x ^{2} + 7 x )}{( x + 7 ) ( x ^{2} + 5 x - 24 )}

Factor

x^{2} + 7 x : x (x + 7)

= \frac{x ( x - 3 ) x ( x + 7 )}{( x + 7 ) ( x ^{2} + 5 x - 24 )}

Apply exponent rule:

aa = a^{2}

xx = x^{2}

= \frac{x ^{2} ( x - 3 ) ( x + 7 )}{( x + 7 ) ( x ^{2} + 5 x - 24 )}

Cancel the common factor:

x + 7

= \frac{x ^{2} ( x - 3 )}{x ^{2} + 5 x - 24}

Factor

x^{2} + 5 x - 24 : (x - 3) (x + 8)

= \frac{x ^{2} ( x - 3 )}{( x - 3 ) ( x + 8 )}

Cancel the common factor:

x - 3

= \frac{x ^{2}}{x + 8}

(- 2 x + 2)^{2}

(2 x - 3) (x + 7)

(6 x^{2}) (- 3 x^{5})

2 x (2 x)

50!

What is (x^3-9x)/(x^2+10x+21)*(x^2+7x)/(x^2+5x-24) ?
The solution to (x^3-9x)/(x^2+10x+21)*(x^2+7x)/(x^2+5x-24) is (x^2)/(x+8)