I can see why the answer to the attached problem is ‘c’. However, how does this reconcile with the ‘bowtie’ method of getting a common denominator? Because if you try to apply the bowtie method to this problem for the last step of simplification, you get “(p^2+1)/p” as the answer.
if you apply cross multiplication to this expression \frac{p}{q} + \frac{1/q}{p}, you get
- (1/q)x(q) = 1
- (p)*(p) = p²
- new denominator = product of both individual denominators = pq
so the answer would be \frac{1+p^2}{pq}. I think you miscalculated the third step of multiplying both the denominators, am I right?
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