Final answer:
To write the given expression in partial fraction form, we would need to factor the denominator and set up terms for each factor in the partial fraction decomposition. Unfortunately, the original rational function isn't yet simplified enough to directly extract the partial fraction coefficients.
Step-by-step explanation:
The student's question asks how to express the rational function (x³+2x-3) / (x²+7x)(x²+9)(4−x²) in partial fraction form. To rewrite this expression in partial fractions, we must first factor the denominator completely and then set up partial fraction components for each unique factor. The denominator can be factored as (x+7)(x)(x+3)(i)(-i)(2+x)(2-x), noticing that (4-x²) can be written as a difference of squares. After factoring, the partial fraction decomposition will include terms for each of these linear factors and the irreducible quadratic factor (x²+9).
However, since the original function is not immediately decomposable into partial fractions without further simplification or manipulation and no coefficients are provided for the partial fraction form, the answer to the student's question would require further clarification or additional work to complete the partial fraction decomposition.