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因式分解在许多有理数计算,代数式化简、求值中起重要作用.它是一种重要的数学方法,灵活运用分解因式方法在数学问题中进行化简,求值计算,会把复杂问题简单化,往往会其到更有效的收获.下面举例分析,供同学们参考.一、利用因式分解进行有理数运算例1计算(1-1/22)(1-1/32)(1-1/42)…-1/20122解析:原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)…(1-1/2012)(1+1/2012)=1/2×3/2×2/3×4/3×…2012/2011×2012/2011×2011/2012×2013/2012
Factorization plays an important role in many rational numbers, algebraic simplification and evaluation.It is an important mathematical method, and it is easy to use factorization method to simplify and solve mathematical problems, Simplification, often it will be more effective harvest. The following examples for analysis, for reference. First, the use of factorization rational number operation Example 1 (1-1 / 22) (1-1 / 32) (1- 1/42) ... -1 / 20122 Resolution: Original = (1-1 / 2) (1 + 1/2) (1-1 / 3) (1 + 1/3) (1-1 / 2012) (1 + 1/2012) = 1/2 × 3/2 × 2/3 × 4/3 × ... 2012/2011 × 2012/2011 × 2011/2012 × 2013/2012