(a+b)^-1 * (a^-1+b^-1)
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Simplify the following:
(1/a+1/b)/(a+b)
Put each term in 1/a+1/b over the common denominator a b: 1/a+1/b = b/(a b)+a/(a b):
(b/(a b)+a/(a b))/(a+b)
b/(a b)+a/(a b) = (b+a)/(a b):
((b+a)/(a b))/(a+b)
(b+a)/(a b (a+b)) = (a+b)/(a+b)×1/(a b) = 1/(a b):
Answer:= 1/(ab)
(1/a+1/b)/(a+b)
Put each term in 1/a+1/b over the common denominator a b: 1/a+1/b = b/(a b)+a/(a b):
(b/(a b)+a/(a b))/(a+b)
b/(a b)+a/(a b) = (b+a)/(a b):
((b+a)/(a b))/(a+b)
(b+a)/(a b (a+b)) = (a+b)/(a+b)×1/(a b) = 1/(a b):
Answer:= 1/(ab)
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