Reducing fractions used everywhere in the exact sciences, not only for the numerical values of the numerator and denominator, but for the fractions presented in the form of a quotient of two polynomials with variables.
To reduce it should be common fractiondenominator and numerator divided by their greatest common factor. In practice, usually a fraction reduction is carried out in several stages. For numerical fractions "by eye" are assessing on how many you can divide the numerator and denominator. Then divide this number, and then again try to reduce the resulting fraction as long as the numerator and denominator have a common factor.
It follows a simple way to reducefractions - the expansion of the numerator and denominator into prime factors. If immediately detect at least one common factor fails, then begin to sort out the prime numbers and find out if any of them is, to which divided the numerator and denominator of the fraction.
In the case where the fraction represented asPrivate polynomials, polynomials should be factored, using the formulas of abridged multiplication or other means trying to bring them into the shape of the product of monomials. Typically, the ability to properly and quickly pick up the formula of abridged multiplication comes only with experience.