Simplify ((4y-8)/(y+2))÷((y-2)/(y^(2-4)))

$\frac{4 y - 8}{y + 2} \div \frac{y - 2}{y^{2 - 4}}$

To divide by a fraction, multiply by its reciprocal.

$\frac{4 y - 8}{y + 2} \cdot \frac{y^{2 - 4}}{y - 2}$

Simplify terms.

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Factor $4$ out of $4 y - 8$ .

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Factor $4$ out of $4 y$ .

$\frac{4 (y) - 8}{y + 2} \cdot \frac{y^{2 - 4}}{y - 2}$

Factor $4$ out of $- 8$ .

$\frac{4 y + 4 \cdot - 2}{y + 2} \cdot \frac{y^{2 - 4}}{y - 2}$

Factor $4$ out of $4 y + 4 \cdot - 2$ .

$\frac{4 (y - 2)}{y + 2} \cdot \frac{y^{2 - 4}}{y - 2}$

Cancel the common factor of $y - 2$ .

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Factor $y - 2$ out of $4 (y - 2)$ .

$\frac{(y - 2) \cdot 4}{y + 2} \cdot \frac{y^{2 - 4}}{y - 2}$

Cancel the common factor.

$\frac{(y - 2) \cdot 4}{y + 2} \cdot \frac{y^{2 - 4}}{y - 2}$

Rewrite the expression.

$\frac{4}{y + 2} y^{2 - 4}$

Combine $\frac{4}{y + 2}$ and $y^{2 - 4}$ .

$\frac{4 y^{2 - 4}}{y + 2}$

Move $y^{2 - 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Simplify the denominator.

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Subtract $4$ from $2$ .

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

Multiply $- 1$ by $- 2$ .

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

Reorder factors in $\frac{4}{(y + 2) y^{2}}$ .

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

Simplify ((4y-8)/(y+2))÷((y-2)/(y^(2-4)))

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