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Suppose X1 = N1/D1 and X2 = N2/D2 are two rational expressions, where the numerators N1 and N2 and denominators D1 and D2 are simpler expressions. Then X1 * X2 = (N1*N2)/(D1*D2) and X1 / X2 = (N1*D2)/(D1*N2).
Yes, it applies to even multiplication of fractions and rational and irrational numbers.
a rational function.
Yes. Rational functions must contain rational expressions in order to be rational.
Division by a non-zero rational number is equivalent to multiplication by its reciprocal.