Question

1. \\(\frac{x^2 - 5x + 6}{x^2 + 2x - 15}\\)

Explanation:

Step1: Factor numerator and denominator

Factor \(x^{2}-5x + 6\): We need two numbers that multiply to \(6\) and add to \(-5\). Those numbers are \(-2\) and \(-3\), so \(x^{2}-5x + 6=(x - 2)(x - 3)\).

Factor \(x^{2}+2x-15\): We need two numbers that multiply to \(-15\) and add to \(2\). Those numbers are \(5\) and \(-3\), so \(x^{2}+2x - 15=(x + 5)(x - 3)\).

So the fraction becomes \(\frac{(x - 2)(x - 3)}{(x + 5)(x - 3)}\).

Step2: Cancel common factors

We can cancel out the common factor \((x - 3)\) (assuming \(x
eq3\) to avoid division by zero), so we get \(\frac{x - 2}{x + 5}\).

Answer:

\(\frac{x - 2}{x + 5}\) (for \(x
eq3\) and \(x
eq - 5\))