Adding and subtracting algebraic fractions

To add fractions with equal denominators we add the numerators and keep the denominator: a/c + b/c = (a + b)/c; subtraction works the same way: a/c - b/c = (a - b)/c. Fractions with different denominators are first brought to a common denominator, then the numerators are added or subtracted: 3/(2x) + 5/(3x) = 9/(6x) + 10/(6x) = 19/(6x). In subtraction it is very important to put the numerator of the subtrahend in brackets, because its signs change: (x + 1)/(x - 1) - (x - 3)/(x - 1) = (x + 1 - x + 3)/(x - 1) = 4/(x - 1). If possible, we reduce the result. If the denominators are polynomials, we factor them to find the common denominator.