Algebraic fractions. Reducing fractions

A fraction whose numerator and denominator are algebraic expressions is called an algebraic fraction, for example (a + b)/(a - b). The letters in a fraction may take only values that do not make the denominator zero; these are the admissible values, because division by zero is impossible. The basic property of a fraction: multiplying or dividing the numerator and denominator by the same nonzero expression does not change the fraction, that is a/b = am/(bm), m ≠ 0. Using it, we reduce a fraction by a common factor of numerator and denominator. Before reducing, factor the numerator and denominator; only factors can be cancelled, never terms.