f(x)=2x^2-3x-9
g(x)=4x^2-9
Find (f/g)(x)
To find (f/g)(x), we need to divide f(x) by g(x).
f(x) = 2x^2 - 3x - 9
g(x) = 4x^2 - 9
(f/g)(x) = f(x) / g(x)
(f/g)(x) = (2x^2 - 3x - 9) / (4x^2 - 9)
To divide these two polynomials, we can use polynomial long division or synthetic division.
Using polynomial long division, we get:
1/2
_____________________
4x^2 - 9 | 2x^2 - 3x - 9
- (2x^2 - 9)
_____________________
6x - 9
Therefore, (f/g)(x) = 1/2x - 9/(4x^2 - 9)