Question

8/ x²+3x-10 (x²-2x)(5x-10) (x)(x-2)(5)(x-2) 2/ (x+5)(x-2)

Explanation:

Step1: Factor the denominator

First, factor the quadratic expression in the denominator \(x^{2}+3x - 10\). We need to find two numbers that multiply to \(- 10\) and add up to \(3\). The numbers are \(5\) and \(-2\), so \(x^{2}+3x - 10=(x + 5)(x-2)\).

Step2: Simplify the fraction

The original expression is \(\frac{2}{x^{2}+3x - 10}\). Substituting the factored form of the denominator, we get \(\frac{2}{(x + 5)(x-2)}\).

Answer:

\(\frac{2}{(x + 5)(x - 2)}\)