Question

(\frac{3}{n^{2} + 17n + 70} cdot \frac{n + 10}{4})

Explanation:

Step1: Factor the quadratic

Factor \( n^2 + 17n + 70 \). We need two numbers that multiply to \( 70 \) and add to \( 17 \). Those numbers are \( 7 \) and \( 10 \), so \( n^2 + 17n + 70=(n + 7)(n + 10) \).
The expression becomes \( \frac{3}{(n + 7)(n + 10)}\cdot\frac{n + 10}{4} \).

Step2: Cancel common factors

Cancel the common factor \( n + 10 \) (assuming \( n
eq - 10 \) to avoid division by zero).
We are left with \( \frac{3}{(n + 7)\cdot4}=\frac{3}{4(n + 7)} \) or \( \frac{3}{4n+28} \).

Answer:

\(\frac{3}{4(n + 7)}\) (or \(\frac{3}{4n + 28}\))