利用因式分解进行分式的化简和计算,是中考中的常见题型,它不仅考查了同学们对因式分解的掌握情况,而且考查了计算能力.例1(广州市)计算:x2+2x-3/x2-9·x2-5x+6/3x2-x-2.解:原式=(x+3)(x-1)/(x+3)(x-3)·(x-2)(x-3)/(3x+2)(x-1)=x-2/3x+2.点评:本题将各多项式进行因式分解后,可以发现分子分母有公因式,约去公因式,即可达到化简的目的. The use of factorization for the reduction and calculation of fractions is a common question in the examination. It not only examines the masters’ understanding of the factorization but also examines the computational power. Example 1 (Guangzhou) Calculation: x2 +2x-3/x2-9.x2-5x+6/3x2-x-2. Solution: Original = (x+3)(x-1)/(x+3)(x-3).(x -2)(x-3)/(3x+2)(x-1)=x-2/3x+2. Comments: After the factorization of each polynomial in this problem, it can be found that the numerator and denominator have a common factor. Going to the public cause, you can achieve the purpose of simplification.