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Simplify: a*((sqrt(a) + sqrt(b))/(2b*sqrt(a)))^(-1) + b*((sqrt(a) + sqrt(b))/(2a*sqrt(b)))^(-1).

1. 2ab
2. ab
3. 2(a + b)
4. 4ab

Correct answer: 2ab

Solution

Term1 = a*(2b*sqrt(a))/(sqrt a + sqrt b) = 2ab*sqrt(a)/(sqrt a + sqrt b). Term2 = b*(2a*sqrt(b))/(sqrt a + sqrt b) = 2ab*sqrt(b)/(sqrt a + sqrt b). Sum = (2ab*sqrt a + 2ab*sqrt b)/(sqrt a + sqrt b) = 2ab(sqrt a + sqrt b)/(sqrt a + sqrt b) = 2ab.

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