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If $$a \colon b = 3 \colon 4$$ and $$\frac{p}{q}=\frac{a^2+b^2+ab}{a^2+b^2-ab}$$, where $$p, q$$ have no common divisors other than 1, $$p+q$$ is
Correct Answer: 50
Taking $$a=3k$$, $$b=4k$$ gives $$a^2+b^2=25k^2$$ and $$ab=12k^2$$, so $$\frac{p}{q}=\frac{25k^2+12k^2}{25k^2-12k^2}=\frac{37}{13}$$. Since 37 and 13 share no common factor, $$p+q=37+13=50$$.
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