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常言道:“饭要一口一口地吃”.面对千姿百态的分式不等式,如果一时难以“一步到位”达到证明目的,不妨探究“分步法”,分成两步或多步,逐步实现证明目的.1.将分式不等式化为整式不等式例1设x,y,z∈R+,求证:(y+z)x(yx+z)+(z+x)y(zy+x)+(x+y)z(xz+y)≥43.(《数学教学》1992(6),数
As the saying goes: “The meal must be eaten bite-mouthed.” Faced with a variety of fractional inequalities, if it is difficult to achieve “one step in place” to achieve the purpose of proof, may wish to explore the “step-by-step” method, divided into two or more steps, and gradually achieve the purpose of proof .1. Turn fractional inequalities into integer inequalities. Example 1 Let x, y, z∈ R+, verify: (y+z)x(yx+z)+(z+x)y(zy+x)+(x +y)z(xz+y)≥43.(“Mathematics Teaching” 1992(6), number