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{___} \quad \text{(simplify your answer.)}\\

Explanation:

Combine the numerators over the common denominator

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

Simplify the numerator

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

Factor the denominator and reduce the fraction

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

Answer:

Subtract the rational expressions.

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

<blank>\(\frac{1}{x+2}\)</blank> (Simplify your answer.)