SOLUTION: Find all values of x for which the graph of (1/x) lies above graph (1/(x-2))

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find all values of x for which the graph of (1/x) lies above graph (1/(x-2))      Log On


   

Question 1147751: Find all values of x for which the graph of (1/x) lies above graph (1/(x-2))
Answer by greenestamps(13203) About Me  (Show Source):
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The graph of 1/x lies above the graph of 1/(x-2) when

1%2Fx+-+1%2F%28x-2%29%3E+0
%28%28x-2%29-x%29%2F%28x%28x-2%29%29%3E0
-2%2F%28x%28x-2%29%29%3E0

The critical points for this inequality are at x=0 and x=2.

On (-infinity,0) the denominator is positive, so the expression value is negative; the inequality is not satisfied.
On (0,2) the denominator is negative, so the expression value is positive; the inequality IS satisfied.
On (2,infinity) the denominator is again positive, so the expression value is negative; the inequality is not satisfied.

ANSWER: 1/x > 1/(x-2) for 0 < x < 2