Simplify (32-2y^2)/(5y^2-80)

$\frac{32 - 2 y^{2}}{5 y^{2} - 80}$

Simplify the numerator.

Factor $2$ out of $32 - 2 y^{2}$ .

Factor $2$ out of $32$ .

$\frac{2 (16) - 2 y^{2}}{5 y^{2} - 80}$

Factor $2$ out of $- 2 y^{2}$ .

$\frac{2 (16) + 2 (- y^{2})}{5 y^{2} - 80}$

Factor $2$ out of $2 (16) + 2 (- y^{2})$ .

$\frac{2 (16 - y^{2})}{5 y^{2} - 80}$

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

$\frac{2 (4^{2} - y^{2})}{5 y^{2} - 80}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4$ and $b = y$ .

$\frac{2 (4 + y) (4 - y)}{5 y^{2} - 80}$

Simplify the denominator.

Factor $5$ out of $5 y^{2} - 80$ .

Factor $5$ out of $5 y^{2}$ .

$\frac{2 (4 + y) (4 - y)}{5 (y^{2}) - 80}$

Factor $5$ out of $- 80$ .

$\frac{2 (4 + y) (4 - y)}{5 y^{2} + 5 \cdot - 16}$

Factor $5$ out of $5 y^{2} + 5 \cdot - 16$ .

$\frac{2 (4 + y) (4 - y)}{5 (y^{2} - 16)}$

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

$\frac{2 (4 + y) (4 - y)}{5 (y^{2} - 4^{2})}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y$ and $b = 4$ .

$\frac{2 (4 + y) (4 - y)}{5 (y + 4) (y - 4)}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $4 + y$ and $y + 4$ .

Reorder terms.

$\frac{2 (y + 4) (4 - y)}{5 (y + 4) (y - 4)}$

Cancel the common factor.

$\frac{2 (y + 4) (4 - y)}{5 (y + 4) (y - 4)}$

Rewrite the expression.

$\frac{2 (4 - y)}{5 (y - 4)}$

Cancel the common factor of $4 - y$ and $y - 4$ .

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{2 (- 1 (- 4) - y)}{5 (y - 4)}$

Factor $- 1$ out of $- y$ .

$\frac{2 (- 1 (- 4) - (y))}{5 (y - 4)}$

Factor $- 1$ out of $- 1 (- 4) - (y)$ .

$\frac{2 (- 1 (- 4 + y))}{5 (y - 4)}$

Reorder terms.

$\frac{2 (- 1 (y - 4))}{5 (y - 4)}$

Cancel the common factor.

$\frac{2 (- 1 (y - 4))}{5 (y - 4)}$

Rewrite the expression.

$\frac{2 \cdot (- 1)}{5}$

Multiply $2$ by $- 1$ .

$\frac{- 2}{5}$

Move the negative in front of the fraction.

$- \frac{2}{5}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{5}$

Decimal Form:

$- 0.4$

Simplify (32-2y^2)/(5y^2-80)

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