Algebraic fractions. Reducing fractions

A fraction whose numerator and denominator are algebraic expressions is called an algebraic fraction, for example (a + b)/(a - b). Putting numbers in place of the letters gives its numerical value, but the denominator must not become zero: in (a + b)/(a - b) we need a ≠ b. The values that keep the denominator non-zero are admissible values; in later topics the letters take only admissible values. The basic property of a fraction: a/b = ma/mb with b ≠ 0, m ≠ 0, i.e. multiplying or dividing the numerator and denominator by the same non-zero expression does not change the fraction. On this basis a fraction is reduced by the common factor of the numerator and denominator; for this we first factor them. Changing the sign of the numerator or of the denominator changes the sign of the fraction: (a - b)/(b - a) = -1.