Final answer:
The sum of 7x/x^2-4 and 2/x+2 is (9x - 4)/(x^2-4) after finding a common denominator and combining like terms.
Step-by-step explanation:
The question asks to find the sum of two algebraic fractions: 7x/x^2-4 and 2/x+2. To find the sum, we need a common denominator. The denominator x^2-4 is a difference of squares that factors into (x+2)(x-2). By using this common denominator, we add the fractions.
First, express the second fraction with the common denominator:
2/(x+2) = (2(x-2))/(x^2-4)
Now, sum the fractions:
(7x + 2(x-2))/(x^2-4)
Simplify the numerator and combine like terms:
(7x + 2x - 4)/(x^2-4)
(9x - 4)/(x^2-4)
This is the simplified sum of the given fractions.