Question

1. \\(\frac{x^2 - 4}{x^2 + 3x - 10}\\)

Explanation:

Step1: Factor numerator and denominator

The numerator \(x^2 - 4\) is a difference of squares, so it factors as \((x - 2)(x + 2)\).
The denominator \(x^2 + 3x - 10\) factors by finding two numbers that multiply to \(-10\) and add to \(3\), which are \(5\) and \(-2\). So it factors as \((x + 5)(x - 2)\).

So the expression becomes \(\frac{(x - 2)(x + 2)}{(x + 5)(x - 2)}\).

Step2: Cancel common factors

We can cancel the common factor \((x - 2)\) (assuming \(x
eq 2\) to avoid division by zero).

This leaves us with \(\frac{x + 2}{x + 5}\).

Answer:

\(\frac{x + 2}{x + 5}\) (for \(x
eq 2\) and \(x
eq -5\))