You can put this solution on YOUR website! X-4
---------- > 0
X^2-3X-10 -
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Put it in factor form:
(x-4)/[(x-5)(x+2)] >=0
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Graph the EQUALITY to establish the boundary for the INEQUALITY:
Notice:
vertical asymptotes at x = 5 and at x = -2
horizontal asymptote is y = 0 because the degree of the
denominator is greater than the degree of the numerator.
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y-intercept at -4/-10 = 2/5
x-intercept at x = 4
Now sketch the curve
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Pick several check points to see where the INEQUALITY area is:
Test in (x-4)/[(x-5)(x+2)] > 0
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(0,0)::::: -4/[(2)(-5)] > 0 ; true ; so that region is solution area
(-10,-10): -14/[(-15)(-8)>0 ; false; so that region is not a solution area
(10,10)::: 6/[(5)(12)] > 0 ; true; so that region is solution area
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Cheers,
Stan H.
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