Question 902235
First for any rational inequality, find the critical points where the numerator or the denominator equal zero.
In this case,
{{{x+10=0}}}
{{{x=-10}}}
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{{{x-17=0}}}
{{{x=17}}}
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So now break up the number line into three regions based on these critical numbers.
Values where the denominator equals zero are values that are not in the domain of the function since division by zero is undefined. 
So for those values use (). 
Region 1 : ({{{infinity}}},{{{-10}}}]
Region 2 : [{{{-10}}},{{{17}}})
Region 3 : ({{{17}}},{{{infinity}}})
For each region choose a point in the region (avoid the endpoints) and test the inequality. 
If the inequality is satisfied, that region is part of the solution.
Otherwise, that region is not part of the solution.
Region 1 : Choose {{{x=-11}}}
{{{(-11+10)/(-11-17)^2>=0}}}
{{{-1/(-38)^2>=0}}}
False, Region 1 is not part of the solution region.
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Region 2 : Choose {{{x=0}}}
{{{(10)/(10-17)^2>=0}}}
{{{(10)/(7)^2>=0}}}
True, Region 2 is part of the solution region.
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Region 3 : Choose {{{x=18}}}
{{{(18+10)/(18-17)^2>=0}}}
{{{28>=0}}}
True, Region 3 is part of the solution region.
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So the solution region is

[{{{-10}}},{{{17}}})U ({{{17}}},{{{infinity}}})
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In terms of table of signs,
{{{matrix(4,4,Term , -11,0,18,Numerator,N,P,P,Denominator,P,P,P,LHS,N,P,P))}}}
where LHS is Left Hand side of the equation, N is negative, P is positive.