Question

simplify the following rational expression.

\\\frac{2x^2 + 7x - 4}{x^2 + 7x + 12}\\

\\\frac{?x - }{x + }\\

Explanation:

Factor the numerator

Using the Factoring Trinomials knowledge point

$$ 2x^2 + 7x - 4 = (2x - 1)(x + 4) $$

Factor the denominator

Using the Factoring Trinomials knowledge point

$$ x^2 + 7x + 12 = (x + 3)(x + 4) $$

Simplify the rational expression

Using the Simplifying Rational Expressions knowledge point

$$ \frac{2x^2 + 7x - 4}{x^2 + 7x + 12} = \frac{(2x - 1)(x + 4)}{(x + 3)(x + 4)} = \frac{2x - 1}{x + 3} \quad (x eq -4) $$

Identify the missing values

Comparing the simplified expression \(\frac{2x - 1}{x + 3}\) with the template \(\frac{[?]x - [ ]}{x + [ ]}\):

• The coefficient of \(x\) in the numerator is \(2\).
• The constant subtracted in the numerator is \(1\).
• The constant added in the denominator is \(3\).

Answer:

Simplify the following rational expression.

$$ \frac{2x^2 + 7x - 4}{x^2 + 7x + 12} $$

The simplified expression is <blank>\(\frac{2x - 1}{x + 3}\)</blank>.