探究与零有关的限制条件

• 作 者: 刘辉
• 机 构: 江苏省扬州梅苑双语学校,
• 出 处: 理科考试研究
• 发表日期: 2014年14期
• 关键词: 限制条件 分母 数学表达式 函数关系式 等腰三角形 取值范围 理解概念 解题 分式 变量 周长 试写 剖析 分子 初中 边长

在初中数学表达式中,与零有关的限制条件是满足定义、性质的重要前提.如不深刻理解概念,并从正、反方面把握其实质,在解题中忽略这些与零有关的限制,就会出错解与漏解.例1当x=时,分式|x|-1x2-2x-3的值为零.错解由|x|-1=0,解得x=±1.剖析当分子为零,且分母不为零时,分式的值为零,显然,当x=-1时,分母x2-2x-3=0.解题中忽略了分母的限制条件.所以正确答案是x=1.

In the math expression of junior high school, the zero-related restriction is an important precondition to satisfy the definition and nature.If we do not deeply understand the concept and grasp its essence from the positive and negative aspects, we neglect these zero-related restrictions in the problem-solving, It will be wrong solution and leak solution.Example 1 When x =, fractional | x | -1x2-2x-3 value is zero. The wrong solution by | x | -1 = 0, solution x = ± 1. Analysis When the numerator is zero and the denominator is not zero, the fractional value is zero. Obviously, when x = -1, the denominator x2-2x-3 = 0. The denominator is neglected in the problem solving, so the correct answer Is x = 1.