Question

simplify. note that you can factor the numerator first and cancel.
\\(\frac{f^2 + 7f + 10}{f + 2}\\)
\\(\circ\\) \\(f + 5\\)
\\(\circ\\) \\(f + 5 + f\\)
\\(\circ\\) \\(\frac{f + 7}{2} + \frac{5}{f}\\)
\\(\circ\\) \\(f + 2\\)

Explanation:

Step1: Factor the numerator

We factor the quadratic expression \(f^2 + 7f + 10\). We need two numbers that multiply to \(10\) and add up to \(7\). The numbers are \(2\) and \(5\), so \(f^2 + 7f + 10=(f + 2)(f + 5)\).
So the expression becomes \(\frac{(f + 2)(f + 5)}{f + 2}\).

Step2: Cancel common factors

We cancel out the common factor \((f + 2)\) in the numerator and the denominator (assuming \(f
eq - 2\) to avoid division by zero).
After canceling, we are left with \(f + 5\).

Answer:

A. \(f + 5\)