增根与无解是分式方程中常见的两个概念,同学们常常会对这两个概念混淆不清,现举例说明它们之间的区别和联系.例1解方程6/(x-1)-(x+5)/(x(x-1))+3/x=0解方程两边都乘以x(x-1),得6x-(x+5)+3(x-1)=0.解这个方程,得x=1经检验,当x=1时,x(x-城)=0,所以x=1是原方程的增根.∴原方程无解.点评显然原方程中未知数、的取值范面是x≠0 Incremental roots and no solutions are two common concepts in fractional equations. Students often confuse these two concepts and illustrate the differences and relations between them. Example 1 Solving Equation 6 / (x-1 ) - (x + 5) / (x (x-1)) + 3 / x = 0 The equation is multiplied by x (x- 1) on both sides to get 6x- (x + 5) +3 (x- 1) = 0. Solve this equation, we have x = 1 After testing, when x = 1, x (x-city) = 0, so x = 1 is the root of the original equation. ∴ original equation no solution. In the unknowns, the value of the range is x ≠ 0