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1.巧施约分。实现通分[例1]计算x2+2xy+y2/x2y+xy2-x2-2xy+y2/x2y-xy2. 分析将算式中的两个分式的分子、分母分别分解因式,约去公因式就可使两个分式的分母相同.解原式=(x+y)2/xy(x+y)-(x-y)2/xy(x-y) =x+y/xy-x-y/xy=(x+y)-(x-y)/xy
1. Coincidence approx. Realize the generalization [Example 1] Calculate x2+2xy+y2/x2y+xy2-x2-2xy+y2/x2y-xy2. Analyze the factors and denominators of the two fractions in the formula. The formula makes the denominator of the two fractions the same. Solution primitive = (x+y)2/xy(x+y)-(xy)2/xy(xy) =x+y/xy-xy/xy= (x+y)-(xy)/xy