Question 322251
Break up the number line into 4 regions.
Region 1:({{{-infinity}}},{{{-3}}})
Region 2:({{{-3}}},{{{0}}}]
Region 3:[{{{0}}},{{{8}}})
Region 4:({{{8}}},{{{infinity}}})
The regions cannot contain {{{x=-3}}} and {{{x=8}}} since there is a discontinuity at those points. 
Hence the use of "(" and ")" instead of "[" and "]" at those points.
Choose a point in each region (not an endpoint) and test the inequality.
If the point satisfies the inequality, the region is part of the solution region.
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Region 1: Let {{{x=-5}}}
{{{5x/((x-8)(x+3))>=0}}}
{{{-25/((-13)(-2))>=0}}}
{{{-25/26>=0}}}
False, Region 1 is not in the solution region. 
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Region 2: Let {{{x=-2}}}
{{{5x/((x-8)(x+3))>=0}}}
{{{-10/((-10)(1))>=0}}}
{{{1>=0}}}
True, Region 2 is part of the solution region.
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Region 3: Let {{{x=5}}}
{{{5x/((x-8)(x+3))>=0}}}
{{{25/((-3)(8))>=0}}}
{{{-25/24>=0}}}
False, Region 3 is not part of the solution region.
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Region 4: Let {{{x=10}}}
{{{5x/((x-8)(x+3))>=0}}}
{{{50/((2)(13))>=0}}}
{{{50/26>=0}}}
True, Region 4 is part of the solution region.
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Solution Region:({{{-3}}},{{{0}}}] U ({{{8}}},{{{infinity}}})
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Graphical verification with h(x) plotted.
Look for regions where {{{h(x)>=0}}}
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{{{drawing(300,300,-10,10,-10,10,blue(line(-3,-10,-3,10)),blue(line(8,-10,8,10)),grid(1),graph(300,300,-10,10,-10,10, 5x/((x-8)(x+3))))}}}