Question 1185633
<br>
{{{f(x)>g(x)}}}
{{{f(x)-g(x)>0}}}
{{{1/x-1/(x-7)>0}}}<br>
Add the two fractions with a common denominator<br>
{{{((x-7)-x)/(x(x-7))>0}}}
{{{(-7)/(x(x-7))>0}}}<br>
The denominator, and therefore the whole expression, changes sign at x=0 and x=7.<br>
(-infinity,0): both factors in the denominator are negative, so the denominator is positive, so the expression is negative.  The inequality is not satisfied.<br>
(0,7): one of the factors in the denominator is negative, so the denominator is negative, so the expression is positive.  The inequality is satisfied.<br>
(7, infinity): both factors in the denominator are positive, so the denominator is positive, so the expression is negative.  The inequality is not satisfied.<br>
ANSWER: The graph of f(x) (red) lies above the graph of g(x) (green) on the interval (0,7)<br>
{{{graph(400,400,-10,10,-2,2,1/x,1/(x-7))}}}<br>