Final answer:
The sum of the rational expressions (6y²+6y+11)/(4y²-11y-3) + (2y²+8y-8)/(4y²-11y-3) is (8y² + 14y + 3) / (4y² - 11y - 3) after combining like terms over the common denominator.
Step-by-step explanation:
To add the rational expressions (6y²+6y+11)/(4y²-11y-3) + (2y²+8y-8)/(4y²-11y-3), we observe that the denominators are the same. Since the denominators are identical, we can combine the numerators directly over the common denominator. This makes the process of adding these expressions much simpler.
The sum of the two rational expressions is:
((6y²+6y+11) + (2y²+8y-8)) / (4y²-11y-3)
To combine the numerators, we add the like terms:
(6y² + 2y²) + (6y + 8y) + (11 - 8)
Which simplifies to:
8y² + 14y + 3 over the common denominator 4y² - 11y - 3, resulting in:
(8y² + 14y + 3) / (4y² - 11y - 3)