If 3/(x + y) + 2/(x - y) = 2 and 9/(x + y) - 4/(x - y) = 1 then

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bb(x = $\frac{5}{2}$, y = $\frac{1}{2}$) Explanation: Put u = 1/(x + y) and v = 1/(x - y). Then the system becomes 3u + 2v = 2 and 9u – 4v = 1. Multiply the first by 2 and add to the second: (6u + 4v) + (9u – 4v) = 4 + 1 $\Rightarrow$ 15u = 5 $\Rightarrow$ u = $\frac{1}{3}$ From 3u + 2v = 2 $\Rightarrow$ 1 + 2v = 2 $\Rightarrow$ v = $\frac{1}{2}$ So, x + y = 3 and x – y = 2. $\Rightarrow$ `x = (3 + 2)/2 = $\frac{5}{2}$, y = (3 - 2)/2 = $\frac{1}{2}$`

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