Simplify. $$ \frac{u-8}{u^{2}-16 u+64} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{u - 8}{u^{2} - 16u + 64}
$$

**Step 1: Factor the Denominator**

First, factor the quadratic expression in the denominator:

$$
u^2 - 16u + 64
$$

This quadratic can be written as a perfect square:

$$
u^2 - 16u + 64 = (u - 8)^2
$$

**Step 2: Simplify the Expression**

Now, substitute the factored form back into the original expression:

$$
\frac{u - 8}{(u - 8)^2}
$$

Simplify by canceling out one $$(u - 8)$$ from the numerator and the denominator:

$$
\frac{1}{u - 8}
$$

**Final Answer:**

$$
\boxed{\dfrac{1}{\,u-8\,}}
$$
$$ \frac{1}{u - 8} $$

Simplify.