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If 1/x + 1/y = 3 and 1/x - 1/y = 7, what is the value of x + y? Express your answer as a common fraction.

 Feb 21, 2021
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Let \(\frac{1}{x} = a\) and \(\frac{1}{y} = b..\)

 

We can rewrite the system like so:

 

a + b = 3

a - b = 7

 

Adding, we get a = 5 and b = -2, which means that x = 1/5 and y = -1/2.

 

x + y = -3/10

 Feb 21, 2021

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