Simplify the sum or difference. State any restrictions on the variable.
3x/(x^2 - 4) + 6/(x+2)
To simplify the sum, find a common denominator for the two fractions:
3x/(x^2 - 4) + 6/(x+2)
= 3x/((x+2)(x-2)) + 6/(x+2)
= (3x + 6(x-2))/((x+2)(x-2))
= (3x + 6x - 12)/((x+2)(x-2))
= (9x - 12)/(x^2 - 4)
The restrictions on the variable x in this case are x cannot equal -2 or 2, because the denominator cannot be equal to zero.