Question

add: $\frac{x^{2}+6x+2}{5x+15} + \frac{x+10}{5x+15}$

1. rewrite the expression as a single fraction.
2. combine like terms.
3. simplify.

Explanation:

Step1: Combine into single fraction

Since the denominators are identical, add the numerators over the common denominator:
$\frac{x^2 + 6x + 2 + x + 10}{5x + 15}$

Step2: Combine like terms in numerator

Combine the linear $x$-terms and constant terms:
$\frac{x^2 + (6x + x) + (2 + 10)}{5x + 15} = \frac{x^2 + 7x + 12}{5x + 15}$

Step3: Factor numerator and denominator

Factor the quadratic numerator and factor out the GCF from the denominator:
$\frac{(x + 3)(x + 4)}{5(x + 3)}$

Step4: Cancel common factors

Cancel the non-zero common factor $(x + 3)$ from numerator and denominator:
$\frac{x + 4}{5}$ (where $x
eq -3$)

Answer:

$\frac{x + 4}{5}$