Question

1. \\(\frac{a + 7}{a^2 + 6a - 7}\\)

Explanation:

Step1: Factor the denominator

We factor the quadratic expression \(a^2 + 6a - 7\). We need two numbers that multiply to \(-7\) and add to \(6\). Those numbers are \(7\) and \(-1\). So, \(a^2 + 6a - 7=(a + 7)(a - 1)\).
The expression becomes \(\frac{a + 7}{(a + 7)(a - 1)}\).

Step2: Cancel the common factor

We cancel out the common factor \((a + 7)\) from the numerator and the denominator (assuming \(a
eq - 7\) to avoid division by zero).
After canceling, we get \(\frac{1}{a - 1}\).

Answer:

\(\frac{1}{a - 1}\) (for \(a
eq - 7\))