Question

1. \\(\dfrac{x^2 + 2x - 48}{x - 6}\\)

no parenthesis

Explanation:

Step1: Factor the numerator

We need to factor the quadratic expression \(x^{2}+2x - 48\). We look for two numbers that multiply to \(- 48\) and add up to \(2\). The numbers are \(8\) and \(-6\) since \(8\times(-6)=-48\) and \(8 + (-6)=2\). So, \(x^{2}+2x - 48=(x + 8)(x - 6)\).

Step2: Simplify the fraction

Now we have the fraction \(\frac{(x + 8)(x - 6)}{x - 6}\). Assuming \(x
eq6\) (to avoid division by zero), we can cancel out the common factor \((x - 6)\) from the numerator and the denominator. So, \(\frac{(x + 8)(x - 6)}{x - 6}=x + 8\) (for \(x
eq6\)).

Answer:

\(x + 8\) (where \(x
eq6\))