Final answer:
To find the simplified expression for (f(x))/g(x), we multiply the numerators and denominators of f(x) and g(x), respectively. The resulting expression, after expansion and simplification, does not factor in a way that allows further simplification.
Step-by-step explanation:
To find the simplified expression for (f(x))/g(x), we need to divide the function f(x) by g(x). This means we will multiply the numerator of f(x) by the denominator of g(x) and the denominator of f(x) by the numerator of g(x).
The given functions are:
- f(x) = (4x2 + 9x + 5) / (4x2 - x - 5)
- g(x) = (4x2 - 11x - 20) / (x2 - 2x - 8)
To combine them, we have:
(f(x))/g(x) = [(4x2 + 9x + 5) / (4x2 - x - 5)] / [(4x2 - 11x - 20) / (x2 - 2x - 8)]
This is equivalent to multiplying by the reciprocal:
(f(x))*g-1(x) = ((4x2 + 9x + 5)*(x2 - 2x - 8)) / ((4x2 - x - 5)*(4x2 - 11x - 20))
We need to multiply the numerators together and the denominators together, simplifying by common factors as needed. However, in this case, the polynomials do not factor in a way that allows for cancellation of terms.
The final step is simply to expand and simplify the expression as much as possible.