Question

simplify the following rational expression.

\\\frac{x^2 + 3x - 28}{3x - 12}\\

\\\frac{x + ?}{\quad}\\

Explanation:

Factor the numerator trinomial

Using the Factoring Trinomials knowledge point

$$ x^2 + 3x - 28 = (x + 7)(x - 4) $$

Factor the denominator binomial

Using the Simplifying Rational Expressions knowledge point

$$ 3x - 12 = 3(x - 4) $$

Simplify the rational expression

Using the Simplifying Rational Expressions knowledge point

$$ \frac{x^2 + 3x - 28}{3x - 12} = \frac{(x + 7)(x - 4)}{3(x - 4)} = \frac{x + 7}{3} \quad (x eq 4) $$

Answer:

Simplify the following rational expression.

$$\frac{x^2 + 3x - 28}{3x - 12}$$

\(\frac{x + 7}{3}\)