SOLUTION: if 1/x=a+b , 1/y=a-b, x+y=? pls show me how to solve it thanks

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Question 1036064: if 1/x=a+b , 1/y=a-b, x+y=?
pls show me how to solve it thanks
Found 2 solutions by stanbon, fractalier:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
if 1/x=a+b , 1/y=a-b, x+y=?
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Invert both sides to get:
x = 1/(a+b)
y = 1/(a-b)
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x + y = [(a-b)+(a+b)]/(a^2-b^2)
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x+y = (2a)/(a^2-b^2)
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Cheers,
Stan H.
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Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Given that
1%2Fx=a%2Bb and 1%2Fy=a-b
we are able to switch x with a+b and y with a-b...it takes two steps but it is perfectly proper...this gives us
x+=+1%2F%28a%2Bb%29 and y+=+1%2F%28a-b%29
so that
x + y = 1%2F%28a%2Bb%29+%2B+1%2F%28a-b%29
Now to combine these, there is a shortcut, but let us just change both fractions to their common denominator (a+b)(a-b)...like this
=%28a-b%29%2F%28%28a%2Bb%29%28a-b%29%29+%2B+%28a%2Bb%29%2F%28%28a%2Bb%29%28a-b%29%29=
2a%2F%28%28a%2Bb%29%28a-b%29%29