Question

What is the sum? 3y/y^2+7y+10+2/y+2

Answer 1

To find the sum of the expressions, you need to find a common denominator and then combine the two expressions. The final result will be (5y^2 + 20y + 20)/(y^2+7y+10)(y+2).

Step-by-step explanation:

To find the sum of the given expressions, 3y/y^2+7y+10 + 2/y+2, we need to first find a common denominator.

The common denominator for the two expressions is (y^2+7y+10)(y+2).

Next, we can add the two expressions together, keeping the common denominator:

(3y(y+2) + 2(y^2+7y+10))/(y^2+7y+10)(y+2).

We can further simplify the numerator by distributing and combining like terms:

((3y^2 + 6y) + (2y^2 + 14y + 20))/(y^2+7y+10)(y+2).

Combining like terms again, we get:

(5y^2 + 20y + 20)/(y^2+7y+10)(y+2).

Answer 2

`(3y)/(y^2+7y+10) + (2)/(y+2) \\ \\ = (3y)/((y+2)(y+5)) + (2)/(y+2) \\ \\ = (3y)/((y+2)(y+5)) + (2(y+5))/((y+2)(y+5)) \\ \\ = (3y+2(y+5))/((y+2)(y+5)) = (3y+2y+10)/((y+2)(y+5)) \\ \\ = (5y+10)/((y+2)(y+5)) = (5(y+2))/((y+2)(y+5)) \\ \\ = (5)/(y+5)`