Simplify (4-w)/(w^2-8w+16)

$\frac{4 - w}{w^{2} - 8 w + 16}$

Step 1

Factor using the perfect square rule.

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

$\frac{4 - w}{w^{2} - 8 w + 4^{2}}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$8 w = 2 \cdot w \cdot 4$

Rewrite the polynomial.

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

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

$\frac{4 - w}{{(w - 4)}^{2}}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $4 - w$ and ${(w - 4)}^{2}$ .

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

$\frac{- 1 (- 4) - w}{{(w - 4)}^{2}}$

Factor $- 1$ out of $- w$ .

$\frac{- 1 (- 4) - (w)}{{(w - 4)}^{2}}$

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

$\frac{- 1 (- 4 + w)}{{(w - 4)}^{2}}$

Reorder terms.

$\frac{- 1 (w - 4)}{{(w - 4)}^{2}}$

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

$\frac{(w - 4) \cdot - 1}{{(w - 4)}^{2}}$

Cancel the common factors.

Factor $w - 4$ out of ${(w - 4)}^{2}$ .

$\frac{(w - 4) \cdot - 1}{(w - 4) (w - 4)}$

Cancel the common factor.

$\frac{(w - 4) \cdot - 1}{(w - 4) (w - 4)}$

Rewrite the expression.

$\frac{- 1}{w - 4}$

Move the negative in front of the fraction.

$- \frac{1}{w - 4}$