What is (x^2-2x-8)/(x^2+10x+21)*(x+3)/(x-4) ?

The solution to (x^2-2x-8)/(x^2+10x+21)*(x+3)/(x-4) is (x+2)/(x+7)

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simplify (x^2-2x-8)/(x^2+10x+21)*(x+3)/(x-4)

simplify

\frac{x ^{2} - 2 x - 8}{x ^{2} + 10 x + 21} \cdot \frac{x + 3}{x - 4}

\frac{x + 2}{x + 7}

Solution steps

\frac{x ^{2} - 2 x - 8}{x ^{2} + 10 x + 21} \cdot \frac{x + 3}{x - 4}

Apply the fraction rule:

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

= \frac{( x ^{2} - 2 x - 8 ) ( x + 3 )}{( x ^{2} + 10 x + 21 ) ( x - 4 )}

Factor

x^{2} - 2 x - 8 : (x + 2) (x - 4)

= \frac{( x + 2 ) ( x - 4 ) ( x + 3 )}{( x ^{2} + 10 x + 21 ) ( x - 4 )}

Cancel the common factor:

x - 4

= \frac{( x + 2 ) ( x + 3 )}{x ^{2} + 10 x + 21}

Factor

x^{2} + 10 x + 21 : (x + 3) (x + 7)

= \frac{( x + 2 ) ( x + 3 )}{( x + 3 ) ( x + 7 )}

Cancel the common factor:

x + 3

= \frac{x + 2}{x + 7}

- 4 x - 2

\frac{x + 5}{x ^{2} - 25}

- 8 + 12

\frac{1}{2} \cdot x

(x^{a + 1} - 3 x^{a - 2})^{2}

What is (x^2-2x-8)/(x^2+10x+21)*(x+3)/(x-4) ?
The solution to (x^2-2x-8)/(x^2+10x+21)*(x+3)/(x-4) is (x+2)/(x+7)