Question

1. \\(\frac{2 - x}{x^2 + 4x - 12}\\)

Explanation:

Step1: Factor the denominator

We factor the quadratic expression in the denominator \(x^{2}+4x - 12\). We need two numbers that multiply to \(- 12\) and add up to \(4\). The numbers are \(6\) and \(-2\). So, \(x^{2}+4x - 12=(x + 6)(x-2)\).
The expression becomes \(\frac{2 - x}{(x + 6)(x - 2)}\).

Step2: Simplify the numerator

Notice that \(2-x=-(x - 2)\). Substitute this into the expression:
\(\frac{-(x - 2)}{(x + 6)(x - 2)}\)

Step3: Cancel out common factors

We can cancel out the common factor \((x - 2)\) (assuming \(x
eq2\) to avoid division by zero), and we get:
\(-\frac{1}{x + 6}\)

Answer:

\(-\frac{1}{x + 6}\) (for \(x
eq2\) and \(x
eq - 6\))