Simplify the sum. State any restrictions on the variables.
X - 2 / x + 3 + 10x / x^2 - 9
In order to simplify the sum, first combine the fractions:
(X - 2) / (x + 3) + (10x) / (x^2 - 9)
Now, factor the denominator of the second fraction:
(x^2 - 9) = (x + 3)(x - 3)
Combine the fractions by finding a common denominator:
[(X - 2)(x - 3) + 10x(x + 3)] / (x + 3)(x - 3)
Simplify the numerator:
[(x^2 -3x - 2) + (10x^2 + 30x)] / (x + 3)(x - 3)
[11x^2 + 27x - 2] / (x + 3)(x - 3)
So the simplified sum is (11x^2 + 27x - 2) / (x + 3)(x - 3)
There are no restrictions on the variable x.