Question

subtract the rational expressions.

\\\frac{2x - 1}{x^2 + 8x + 12} - \frac{x - 7}{x^2 + 8x + 12}\\

\\\frac{2x - 1}{x^2 + 8x + 12} - \frac{x - 7}{x^2 + 8x + 12} = \text{ } (\text{simplify your answer.})\\

Explanation:

Combine the numerators over the common denominator

Using the Rational Expression Subtraction knowledge point

$$ \frac{2x-1}{x^2+8x+12} - \frac{x-7}{x^2+8x+12} = \frac{(2x-1) - (x-7)}{x^2+8x+12} $$

Simplify the numerator

Using the Rational Expression Subtraction knowledge point

$$ \frac{2x - 1 - x + 7}{x^2+8x+12} = \frac{x+6}{x^2+8x+12} $$

Factor the quadratic denominator

Using the Factoring Quadratics knowledge point

$$ x^2+8x+12 = (x+6)(x+2) $$

Simplify the rational expression

Using the Simplifying Rational Expressions knowledge point

$$ \frac{x+6}{(x+6)(x+2)} = \frac{1}{x+2} \quad (x e -6) $$

Answer:

\(\frac{2x-1}{x^2+8x+12} - \frac{x-7}{x^2+8x+12} =\) <blank>\(\frac{1}{x+2}\)</blank> (Simplify your answer.)