Posted by math help on Sunday, December 5, 2010 at 7:05pm.
Solve x9/x^24 < 0 and write interval notation

algebra  MathMate, Sunday, December 5, 2010 at 9:22pm
Note:
x9/x^24 < 0 ≠ (x9)/(x^24) < 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 lefthandside).
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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