Question 1147751
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The graph of 1/x lies above the graph of 1/(x-2) when<br>
{{{1/x - 1/(x-2)> 0}}}
{{{((x-2)-x)/(x(x-2))>0}}}
{{{-2/(x(x-2))>0}}}<br>
The critical points for this inequality are at x=0 and x=2.<br>
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.<br>
ANSWER: 1/x > 1/(x-2) for 0 < x < 2