Simplify \(\frac{(p - r)^2 - r^2}{2p^2 - 4pr}\)
Question 1 Report
Simplify \(\frac{(p - r)^2 - r^2}{2p^2 - 4pr}\)
Answer Details
First, let's simplify the numerator:
\begin{align*}
(p-r)^2 - r^2 &= (p^2 - 2pr + r^2) - r^2 \\
&= p^2 - 2pr
\end{align*}
Now, let's factor the denominator:
\begin{align*}
2p^2 - 4pr &= 2p(p - 2r)
\end{align*}
Substituting these results, we get:
\begin{align*}
\frac{(p-r)^2 - r^2}{2p^2 - 4pr} &= \frac{p^2 - 2pr}{2p(p - 2r)} \\
&= \frac{p(p-2r)}{2p(p-2r)} \\
&= \frac{1}{2}
\end{align*}
Therefore, the answer is: \boxed{\frac{1}{2}}.
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