Question

week 6 quiz
due sunday by 11:59pm points 100 submitting an externa
question 5 - 1 point
simplify: $\frac{3q^{2}+10q}{3q + 1}+\frac{3}{3q + 1}$
provide your answer below:

Explanation:

Step1: Combine the fractions

Since the denominators are the same ($3q + 1$), we use the rule $\frac{a}{c}+\frac{b}{c}=\frac{a + b}{c}$. So, $\frac{3q^{2}+10q}{3q + 1}+\frac{3}{3q + 1}=\frac{3q^{2}+10q + 3}{3q + 1}$.

Step2: Factor the numerator

Factor $3q^{2}+10q + 3$. We need two numbers that multiply to $3\times3 = 9$ and add up to $10$. The numbers are $9$ and $1$. So, $3q^{2}+10q + 3=3q^{2}+9q+q + 3=3q(q + 3)+1(q + 3)=(3q + 1)(q+ 3)$.

Step3: Simplify the fraction

Substitute the factored - form of the numerator into the fraction: $\frac{(3q + 1)(q + 3)}{3q + 1}$. Cancel out the common factor $(3q + 1)$ in the numerator and the denominator.

Answer:

$q + 3$