Question on: WAEC Mathematics - 2016
Simplify \(\frac{(p - r)^2 - r^2}{2p^2 - 4pr}\)
A
\(\frac{1}{2}\)
B
p - 2r
C
\(\frac{1}{p - 2r}\)
D
\(\frac{2p}{p - 2r}\)
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Correct Option: A
\(\frac{(p - r)^2 - r^2}{2p^2 - 4pr}\)
= \(\frac{(p - r)(p - r) - r^2}{2p^2 - 4pr}\)\
= \(\frac{p^2 - 2pr + r^2 - r^2}{2p(p - 2r}\)
= \(\frac{p^2 - 2pr}{2p(p - 2r)}\)
= \(\frac{p(p - 2r)}{2p(p - 2r)}\)
= \(\frac{1}{2}\)
= \(\frac{(p - r)(p - r) - r^2}{2p^2 - 4pr}\)\
= \(\frac{p^2 - 2pr + r^2 - r^2}{2p(p - 2r}\)
= \(\frac{p^2 - 2pr}{2p(p - 2r)}\)
= \(\frac{p(p - 2r)}{2p(p - 2r)}\)
= \(\frac{1}{2}\)
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