Asked by math help
Solve x-9/x^2-4 < 0 and write interval notation
Answers
Answered by
MathMate
Note:
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
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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