Question 1126016: Solve the inequality using a sign chart. Support graphically. SHow the equations that find the real zeros.
((x-5)/(x^2-36))<0
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
f(x) is 0 at x = 5 only.
f(x) is undefined (so there are vertical asymptotes) at x=-6 and x=6.
The zeros of the numerator and denominator divide the domain into four parts: (-infinity,-6), (-6,5], [5,6), and (6, infinity).
| x+6 x-5 x-6 | f(x)
--------------------------------------------
(-infinity, -6) | - - - | -
(-6,5] | + - - | +
[5,6) | + + - | -
(6, infinity) | + + + | +
The function is negative on (-infinity,-6) and on (5,6); it is 0 at x=5; the value goes to positive or negative infinity close to the vertical asymptotes, at x=-6 and x=6.
The graph...
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