## Algebra: A Combined Approach (4th Edition)

$\dfrac{x}{x^{2}+9x+14}+\dfrac{7}{x^{2}+9x+14}=\dfrac{1}{x+2}$
$\dfrac{x}{x^{2}+9x+14}+\dfrac{7}{x^{2}+9x+14}$ Evaluate the sum of the two rational expressions. Since both expressions have the same denominator, the resulting expression will have the same polynomial in the denominator and its numerator will be the sum of the numerators of the two previous expressions: $\dfrac{x}{x^{2}+9x+14}+\dfrac{7}{x^{2}+9x+14}=\dfrac{x+7}{x^{2}+9x+14}=...$ Factor the denominator and simplify: $...=\dfrac{x+7}{(x+7)(x+2)}=\dfrac{1}{x+2}$