Simplify the sum or difference. State any restrictions on the variable. 3x/x^2-4 + 6/x+2

Answer 1

To simplify the sum or difference, we need a common denominator. Factoring x^2-4 gives us (x+2)(x-2), so we can write:

3x/(x+2)(x-2) + 6/(x+2)

To add these fractions, we need a common denominator of (x+2)(x-2). We can find the equivalent fraction for 6/(x+2) by multiplying the numerator and denominator by (x-2):

3x/(x+2)(x-2) + 6(x-2)/(x+2)(x-2)

Combining the fractions gives:

(3x+6x-12)/(x+2)(x-2) = (9x-12)/(x+2)(x-2)

The restrictions on the variable come from the fact that we cannot divide by zero. Therefore, x cannot be equal to -2 or 2.