document.write( "Question 1147751: Find all values of x for which the graph of (1/x) lies above graph (1/(x-2)) \n" ); document.write( "

Algebra.Com's Answer #769099 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "The graph of 1/x lies above the graph of 1/(x-2) when

\n" ); document.write( " $\"1%2Fx+-+1%2F%28x-2%29%3E+0\"$
\n" ); document.write( " $\"%28%28x-2%29-x%29%2F%28x%28x-2%29%29%3E0\"$
\n" ); document.write( " $\"-2%2F%28x%28x-2%29%29%3E0\"$

\n" ); document.write( "The critical points for this inequality are at x=0 and x=2.

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

\n" ); document.write( "ANSWER: 1/x > 1/(x-2) for 0 < x < 2
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