Posted by ted on .
how do you solve this inequality
3x2 < x+4/x2
please help i don't get it

math 
Reiny,
You must mean:
3x2 < (x+4)/(x2) , so clearly x ≠ 2
(x2)(3x2) < x+4
3x^2  8x + 4  x  4 < 0
3x^2  9x < 0
3x(x3) < 0
So the "critical values" are x=0 , x = 2, and x=3
test for a value of x<0
let x=5 in original
17 < 1/7
17 < 1/7 ? YES
test for a value between 0 and 2
let x=1
1 < 5/1
1 < 5 ? NO
test for a value between 2 and 3
let x = 2.5
5.5 < 6.5/.5
5.5 < 13 ? , YES
test for a value x>3
let x=5
13 < 9/3
13 < 3 ? , NO
so we have x ≤ 0 OR 2 < x ≤ 3 , notice that x=2 in not included
To see that this is correct
go to my favourite graphing program
http://rechneronline.de/functiongraphs/
and enter
3x2  (x+4)/(x2)
in the window for "first graph"
change the "Range yaxis from" entries to 200 to 200
you will see the curve below the xaxis from infinitity to 0
above the xaxis from 0 to the asymptote of 2
below the xaxis from 2 to 3, and
above the xaxis for x>3 
math 
ted,
thanks so much :)

math 
ted,
what if all the values you put in do not work. how would you write the intervals.?

math 
Damon,
If the inequality can not be satisfied for any real value of x, then you just have to say that.