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解分式方程(组),一般都是两边同乘以各个分母的最简公分母,把分式方程化为整式方程再求解。但在分式方程(组)中,还有一些习题直接利用这一般方法来解是很繁杂的,因此需要探究一些特殊解法。现归纳九种方法,供参考。一、换元法这种方法较为常用,课本也作了介绍。这里简单举例说明。例1、解方程x~2+3x-(20/(x~2+3x))=8〔《代数》第三册P_(152)) 解:比较两个式子,含有未知数的项都有x~2+3x,令y=x~2+3x,则原方程化为y-20/y=8。∴y~2-8y-20=0 得y_1=-2,y_2=10。由x~2+3x=-2,解得x_1=-1,x_2=-2, 由x~2+3x=10,解得x_3=-5,x_4=2。经检验这四个值都是原方程的根。
The fractional equations (groups) are generally the simplest common denominator with both sides demultiplexed by each denominator, and the fractional equations are converted into integral equations and then solved. However, in the fractional equations (groups), there are still some problems that can be solved directly using this general method. Therefore, it is necessary to explore some special solutions. The nine methods are summarized for reference. First, the replacement method This method is more commonly used, textbooks have also introduced. Here is a simple example. Example 1. Solution equation x~2+3x-(20/(x~2+3x))=8[Algebra] P(152) Solution: Comparing two equations, items with unknowns have x~2+3x, let y=x~2+3x, then the original equation is y-20/y=8. ∴y~2-8y-20=0 get y_1=-2, y_2=10. From x~2+3x=-2, x_1=-1, x_2=-2, x~2+3x=10, and x_3=-5 and x_4=2. The four values tested are the roots of the original equation.