1963 TMTA High School Algebra I Contest Problem 8

Problem

$\frac{a^{-1} + b^{-1}}{(a+b)^{-1}}$ is equal to

$\text{(A)} \quad \frac{(a+b)^2}{ab} \quad \text{(B)} \quad \frac{1}{ab} \quad \text{(C)} \quad ab \quad \text{(D)} \quad \frac{ab}{(a+b)^2} \quad \text{(E)} a+b$

Solution

$\frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{a+b}} = \frac{\frac{a+b}{ab}}{\frac{1}{a+b}} = \frac{a+b}{ab} \cdot (a+b) = \boxed{\text{(A)} \quad \frac{(a+b)^2}{ab}}$

1963 TMTA High School Mathematics Contests (Problems)
Preceded by Problem 7	TMTA High School Mathematics Contest Past Problems/Solutions	Followed by Problem 9

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1963 TMTA High School Algebra I Contest Problem 8

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