Question

hw prerequisite: rational equations due wednesday by 11:59pm points 100 submitting an external tool question 17 multiply and simplify the following rational expression. (\\(\frac{x^{2}+x - 30}{x^{2}+14x + 45}\\)) \\(\cdot\\) (\\(\frac{x + 9}{x + 6}\\)) give your answer as a reduced rational expression. provide your answer below:

Explanation:

Step1: Factor the quadratic expressions

Factor $x^{2}+x - 30=(x + 6)(x - 5)$ and $x^{2}+14x + 45=(x + 5)(x+9)$.
So the expression becomes $\frac{(x + 6)(x - 5)}{(x + 5)(x + 9)}\cdot\frac{x + 9}{x + 6}$.

Step2: Cancel out the common factors

Cancel out the common factors $(x + 6)$ and $(x + 9)$ in the numerator and denominator.
We get $\frac{x - 5}{x + 5}$.

Answer:

$\frac{x - 5}{x + 5}$