Final answer:
To solve the algebraic fraction equation 3/(x-3) + x/(x+3), we find a common denominator, simplify the resulting equation, and determine that the correct answer is E. (x²+9)/(x²-9).
Step-by-step explanation:
The question involves solving the algebraic fraction equation 3/(x-3) + x/(x+3) and finding which of the given options it equals to. To solve this, we need to find a common denominator so that we can combine the two fractions. The common denominator for (x-3) and (x+3) is their product, which is (x²-9). We multiply the first fraction by ((x+3)/(x+3)) and the second by ((x-3)/(x-3)) to achieve this common denominator.
- Multiply the numerator of the first fraction by (x+3): 3*(x+3) = 3x + 9.
- Multiply the numerator of the second fraction by (x-3): x*(x-3) = x² - 3x.
- Combine the fractions over the common denominator: (3x+9+x²-3x)/(x²-9).
- Simplify the combined fraction: (x²+9)/(x²-9).
Therefore, the correct answer is E. (x²+9)/(x²-9).