What is (d+3)/(d^2)*(3d)/(d^2+7d+12) ?

The solution to (d+3)/(d^2)*(3d)/(d^2+7d+12) is 3/(d(d+4))

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simplify (d+3)/(d^2)*(3d)/(d^2+7d+12)

simplify

\frac{d + 3}{d ^{2}} \cdot \frac{3 d}{d ^{2} + 7 d + 12}

\frac{3}{d ( d + 4 )}

Solution steps

\frac{d + 3}{d ^{2}} \cdot \frac{3 d}{d ^{2} + 7 d + 12}

Apply the fraction rule:

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

= \frac{( d + 3 ) \cdot 3 d}{d ^{2} ( d ^{2} + 7 d + 12 )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

d^{2} = dd

= \frac{( d + 3 ) \cdot 3 d}{dd ( d ^{2} + 7 d + 12 )}

Cancel the common factor:

d

= \frac{( d + 3 ) \cdot 3}{d ( d ^{2} + 7 d + 12 )}

Factor

d^{2} + 7 d + 12 : (d + 3) (d + 4)

= \frac{( d + 3 ) \cdot 3}{d ( d + 3 ) ( d + 4 )}

Cancel the common factor:

d + 3

= \frac{3}{d ( d + 4 )}

\frac{( - 4 d ^{4} ) ^{2}}{- 5 d ^{- 10}}

(6 a^{- 3}) (- 2 a^{4})

\frac{2}{3 7}

\frac{5}{2} \div \frac{1}{2}

What is (d+3)/(d^2)*(3d)/(d^2+7d+12) ?
The solution to (d+3)/(d^2)*(3d)/(d^2+7d+12) is 3/(d(d+4))