Simplify the sum. State any restrictions on the variables.

Question

X - 2 / x + 3 + 10x / x^2 - 9

Answer 1

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.