(1)、(2)的计算与证明,通常是先通分,后计算分子的值,再约去分子、分母的公因式,便得问题的解。但是当分子、分母的因式增多时(即a_i(i>3)的个数较多时),如果仍采用通常的运算方法,显然由于运算复杂而产生困难。本文应用高等代数中的行列式理论与多项式理论,分别对(1)、(2)的一般形式给出两种证明方法。 (1)式的一般形式是: The calculations and proofs of (1) and (2) are usually passed through first, then the value of the numerator is calculated, and the common factor of the denominator and denominator is then approximated to obtain the solution to the problem. However, when the factors of the numerator and the denominator increase (that is, when the number of a_i (i>3) is large), if the usual operation method is still used, it is apparent that the calculation is complicated and difficult. This paper applies the determinant theory and polynomial theory in higher algebra, and gives two kinds of proof methods for the general forms of (1) and (2). The general form of (1) is: