posted by .

4/x^2 - 4x + 3 < 5/x^2 - 9

This is a rational inequality. it is 4 divided by x squared minus 4x plus 3 is less than or equal to 5 divided by x squared minus 9. Please help!!!

Get things organized a bit:

1/x^2 + 4x - 12 > 0
Now, as long as x is not zero, we can multiply by x^2

1 + 4x^3 - 12x^2 > 0

The roots of this cubic are
-0.276, 0.305, 2.972

y>0 on (-0.276,0) (0,0.305) (2.972,+oo)

## Similar Questions

1. ### math

(X^2-1)/(x-1) = (x+1)(x-1)/(x-1) = x+1. If you then subtract your original number, x, you are left with 1. The reason this doesn't work with 1 is that you would have 1-1=0 in the denominator and you cannot divide by zero. This uses …
2. ### Math

A few here. 4x-8 ------ x(squared)-4 _________________________ 2m(squared)+5m-3 ------------------ m(squared)+4m+3 __________________________ 3x+4 ----- 12 (times) 8 ----- 9x+12 ________________________ x+5 ----- 16x (divided by) 3x-2 …
3. ### math 176

please detail all the steps for x squared minus 6xy plus 9y squared minus 4z squared

x squared minus 6xy plus 9y squared minus 4z squared
5. ### Math (College Level Mathematics)

Let c > 0 be a constant. For F E Cp (-C, C), the Bessel inequality is ao squared/ 2 + N E n = 1 (an squared + bn squared) is less than or equal to 1/C { c on top, c on bottom [ f (x)] squared of x, N = 1, 2, ... Where an and bn …
6. ### math

Simplify completely quantity 6 x squared minus 54 plus 84 over quantity 8 x squared minus 40 x plus 48 divided by quantity x squared plus x minus 56 over quantity 2 x squared plus 12 x minus 32
7. ### Calculus

Which of the following integrals cannot be evaluated using a simple substitution?