Simplify (y+4)÷((y^2+8y+16)/(ab))

$(y + 4) \div \frac{y^{2} + 8 y + 16}{a b}$

To divide by a fraction, multiply by its reciprocal.

$(y + 4) \frac{a b}{y^{2} + 8 y + 16}$

Factor using the perfect square rule.

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Rewrite $16$ as $4^{2}$ .

$(y + 4) \frac{a b}{y^{2} + 8 y + 4^{2}}$

Check the middle term by multiplying $2 a b$ and compare this result with the middle term in the original expression.

$2 a b = 2 \cdot y \cdot 4$

Simplify.

$2 a b = 8 y$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = y$ and $b = 4$ .

$(y + 4) \frac{a b}{{(y + 4)}^{2}}$

Cancel the common factor of $y + 4$ .

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Factor $y + 4$ out of ${(y + 4)}^{2}$ .

$(y + 4) \frac{a b}{(y + 4) (y + 4)}$

Cancel the common factor.

$(y + 4) \frac{a b}{(y + 4) (y + 4)}$

Rewrite the expression.

$\frac{a b}{y + 4}$

Simplify (y+4)÷((y^2+8y+16)/(ab))

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