Final answer:
The correct form of the partial fraction decomposition is 7x / (x(x + 9)) + 18 / (x(x + 9)).
Step-by-step explanation:
The expression 7x + 18 / (x^2 + 9x) can be rewritten as a fraction. To do this, we need to perform a partial fraction decomposition. The expression can be decomposed into two fractions:
7x / (x^2 + 9x) + 18 / (x^2 + 9x)
Now, we can split both fractions further by factoring out the common denominator:
7x / (x(x + 9)) + 18 / (x(x + 9))
Thus, the correct form of the partial fraction decomposition for the expression 7x + 18 / (x^2 + 9x) is:
7x / (x(x + 9)) + 18 / (x(x + 9))