What is (x^2+2x-24)/(x^2-9)\times (x+3)/(x^2-16) ?

The solution to (x^2+2x-24)/(x^2-9)\times (x+3)/(x^2-16) is (x+6)/((x-3)(x+4))

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simplify (x^2+2x-24)/(x^2-9)\times (x+3)/(x^2-16)

simplify

\frac{x ^{2} + 2 x - 24}{x ^{2} - 9} \cdot \frac{x + 3}{x ^{2} - 16}

\frac{x + 6}{( x - 3 ) ( x + 4 )}

Solution steps

\frac{x ^{2} + 2 x - 24}{x ^{2} - 9} \cdot \frac{x + 3}{x ^{2} - 16}

Apply the fraction rule:

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

= \frac{( x ^{2} + 2 x - 24 ) ( x + 3 )}{( x ^{2} - 9 ) ( x ^{2} - 16 )}

Factor

x^{2} - 9 : (x + 3) (x - 3)

= \frac{( x ^{2} + 2 x - 24 ) ( x + 3 )}{( x + 3 ) ( x - 3 ) ( x ^{2} - 16 )}

Cancel the common factor:

x + 3

= \frac{x ^{2} + 2 x - 24}{( x - 3 ) ( x ^{2} - 16 )}

Factor

x^{2} + 2 x - 24 : (x - 4) (x + 6)

= \frac{( x - 4 ) ( x + 6 )}{( x - 3 ) ( x ^{2} - 16 )}

Factor

x^{2} - 16 : (x + 4) (x - 4)

= \frac{( x - 4 ) ( x + 6 )}{( x - 3 ) ( x + 4 ) ( x - 4 )}

Cancel the common factor:

x - 4

= \frac{x + 6}{( x - 3 ) ( x + 4 )}

\frac{- 4 - 4 i}{10 - 2 i}

\frac{cot ^{2} ( x )}{csc ( x )} - csc (x)

\frac{1}{x ^{2}} \cdot x

(x + 13)^{2}

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

What is (x^2+2x-24)/(x^2-9)\times (x+3)/(x^2-16) ?
The solution to (x^2+2x-24)/(x^2-9)\times (x+3)/(x^2-16) is (x+6)/((x-3)(x+4))