what is the sum?\n$\frac{3y}{y^{2}+7y + 10}+\frac{2}{y + 2}$\n$\frac{5}{y - 5}$\n$\frac{5(y + 2)}{(y - 2)(y…

Explanation:

Step1: Factor the denominator

Factor $y^{2}+7y + 10$ as $(y + 2)(y+5)$. So the expression becomes $\frac{3y}{(y + 2)(y + 5)}+\frac{2}{y + 2}$.

Step2: Find a common - denominator

The common denominator of the two fractions is $(y + 2)(y + 5)$. Rewrite $\frac{2}{y + 2}$ as $\frac{2(y + 5)}{(y + 2)(y + 5)}$.

Step3: Add the fractions

$\frac{3y}{(y + 2)(y + 5)}+\frac{2(y + 5)}{(y + 2)(y + 5)}=\frac{3y+2(y + 5)}{(y + 2)(y + 5)}$.

Step4: Simplify the numerator

Expand $3y+2(y + 5)$: $3y+2y+10 = 5y+10=5(y + 2)$. So the fraction is $\frac{5(y + 2)}{(y + 2)(y + 5)}$.

Step5: Cancel out the common factor

Cancel out the common factor $(y + 2)$ in the numerator and denominator. We get $\frac{5}{y + 5}$.

Answer:

$\frac{5}{y + 5}$