SOLUTION: Solve for the variable. Show all work please. Please also include a check. If the solution is undefined please say so. Thanks :) (x-2)/(x+1)=(x+1)/(x-2)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve for the variable. Show all work please. Please also include a check. If the solution is undefined please say so. Thanks :) (x-2)/(x+1)=(x+1)/(x-2)      Log On


   



Question 676233: Solve for the variable. Show all work please. Please also include a check. If the solution is undefined please say so. Thanks :)
(x-2)/(x+1)=(x+1)/(x-2)

Found 2 solutions by stanbon, swincher4391:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(x-2)/(x+1)=(x+1)/(x-2)
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Cross-multiply to get:
x^2-4x+4 = x^2+2x+1
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Subtract x^2 from both sides:
Add 4x to both sides
Subtract 1 from both sides
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6x = 3
Divide both sides by 6 to get:
x = 1/2
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Cheers,
Stan H.

Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Cross multiply to get:
%28x-2%29%5E2+=+%28x%2B1%29%5E2
Take the square root:
x-2+=++x%2B1
Take all four combinations of plus and minus to find that
-x + 2 = x + 1
2x = 1
x = 1/2