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December 21, 2014

December 21, 2014

Posted by **math help** on Sunday, December 5, 2010 at 7:05pm.

- algebra -
**MathMate**, Sunday, December 5, 2010 at 9:22pmNote:

x-9/x^2-4 < 0 ≠ (x-9)/(x^2-4) < 0

I presume it is the latter, and that you have omitted to insert parentheses when interpreting a fraction.

The best way to visualize the problem is to sketch a graph of the function (of the left-hand-side).

The numerator is positive for x>9, and negative for x<9.

The denominator is >0 for |x|>2, and <0 for x<2.

Note that there is a vertical asymptote at x=2.

So make a table:

interval numerator denominator expression

(-∞,-2) <0 >0 <0

(-2,2) <0 <0 >0

(2,9) <0 >0 <0

(9,+∞) >0 >0 >0

From the table, it should be relatively easy to find the solution to f(x)<0.

For reference:

http://img811.imageshack.us/img811/4262/1291593942.png

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