Algebraic fractions extend the concept of a numerical fraction: instead of numbers we have polynomials. The chapter starts from the definition of an algebraic fraction as the ratio of two polynomials and from its existence conditions, obtained by requiring the denominator to be non-zero. From here all the factorisation techniques already met become indispensable: they are needed to simplify fractions by recognising the special products and to carry out the operations (addition, subtraction, product and quotient) by reducing the fractions to the least common multiple of the denominators.