SOLUTION: x+1/x=5, find the value of x/x^2+x+1

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Question 1036158: x+1/x=5, find the value of x/x^2+x+1
Answer by ikleyn(52780) About Me  (Show Source):
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x+1/x=5, find the value of x/x^2+x+1
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Instead of x%2F%28x%5E2+%2B+x+%2B+1%29, let us consider its reciprocal %28x%5E2+%2B+x+%2B+1%29%2Fx.


It is equal to x+%2B+1+%2B+1%2Fx    (1).


Since x+%2B+1%2Fx = 5  (given !), we have for (1) x+%2B+1+%2B+1%2Fx = 5 + 1 = 6.


Therefore,  x%2F%28x%5E2+%2B+x+%2B+1%29 = 1%2F6.