What is (x^2+8x+15)/(x-4)*(x^2-16)/(2x+6) ?

The solution to (x^2+8x+15)/(x-4)*(x^2-16)/(2x+6) is ((x+5)(x+4))/2

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simplify (x^2+8x+15)/(x-4)*(x^2-16)/(2x+6)

simplify

\frac{x ^{2} + 8 x + 15}{x - 4} \cdot \frac{x ^{2} - 16}{2 x + 6}

\frac{( x + 5 ) ( x + 4 )}{2}

Solution steps

\frac{x ^{2} + 8 x + 15}{x - 4} \cdot \frac{x ^{2} - 16}{2 x + 6}

Apply the fraction rule:

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

= \frac{( x ^{2} + 8 x + 15 ) ( x ^{2} - 16 )}{( x - 4 ) ( 2 x + 6 )}

Factor

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

= \frac{( x ^{2} + 8 x + 15 ) ( x + 4 ) ( x - 4 )}{( x - 4 ) ( 2 x + 6 )}

Cancel the common factor:

x - 4

= \frac{( x ^{2} + 8 x + 15 ) ( x + 4 )}{2 x + 6}

Factor

x^{2} + 8 x + 15 : (x + 3) (x + 5)

= \frac{( x + 3 ) ( x + 5 ) ( x + 4 )}{2 x + 6}

Factor

2 x + 6 : 2 (x + 3)

= \frac{( x + 3 ) ( x + 5 ) ( x + 4 )}{2 ( x + 3 )}

Cancel the common factor:

x + 3

= \frac{( x + 5 ) ( x + 4 )}{2}

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

\frac{2}{3} \div \frac{8}{9}

\frac{x ^{- 1} + y ^{- 1}}{x + y}

(x + 1) - 1

(s + 1) (s^{2} + 6 s + 13)

What is (x^2+8x+15)/(x-4)*(x^2-16)/(2x+6) ?
The solution to (x^2+8x+15)/(x-4)*(x^2-16)/(2x+6) is ((x+5)(x+4))/2