Final answer:
Therefore, the correct answer is D. x = -3 and x = 3; Sum = -2.
Step-by-step explanation:
To find the sum of the solutions to the equation, multiply the equation by the common denominator and simplify. Then, factor the quadratic equation to find the solutions. Finally, add the solutions to find the sum.
The given equation is: 1/x-2 + 3/x+3 = 4/x²+x-6
To find the sum of the solutions, we need first to find the roots of the equation.
Let's multiply all terms by (x-2)(x+3)(x²+x-6) (the common denominator).
After simplifying and rearranging the equation, we get x² + 2x - 3 = 0
Factoring the quadratic equation, we have (x+3)(x-1) = 0
This gives us two solutions: x = -3 and x = 1
The sum of the solutions is -3 + 1 = -2
Therefore, the correct answer is: D. x = -3 and x = 3; Sum = -2