Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\frac{1}{u - 8}
\]
Solution
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:**
\[
\boxed{\dfrac{1}{\,u-8\,}}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To simplify the expression \(\frac{u-8}{u^{2}-16u+64}\), we start by factoring the denominator. Notice that the denominator can be rewritten: \[ u^{2} - 16u + 64 = (u - 8)^{2} \] Now, we substitute this back into the expression: \[ \frac{u-8}{(u - 8)^{2}} \] Next, we can simplify by canceling one \(u - 8\) from the numerator and the denominator: \[ \frac{1}{u - 8} \quad \text{for } u \neq 8 \] Thus, the simplified expression is: \[ \frac{1}{u - 8} \]
