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分式的基本性质:分式的分子和分母同时乘以或除以同一个不为0的整式,分式的值不变.常在代数变形中使用,用之解几何题同样可收到意想不到的效果,请看一例:题目(文(1)第586页例2)如图,将矩形ABCD的四个角向内折起,恰好拼成一个既无缝隙又无重叠的四边形EFGH,若EH=3、EF=4,那么线段AD与AB的比等于().常规方法见文(1),纯粹几何计算法.本文解法思路目标求AD AB.由分式的基本性质有AD AB=AD·AD AB·AD=AD2AB·AD,不难发现分母AB·AD表示矩形ABCD
The basic nature of the fractional formula: the numerator and denominator of a fraction are multiplied or divided by the same integer not equal to zero, and the value of the fractional value is unchanged. Often used in algebraic deformation, Unexpected effects, see an example: subject (article (1) p. 586 Example 2) Figure 4, the four corners of the rectangular ABCD fold inward, just spell into a seamless and non-overlapping quadrilateral EFGH, if EH = 3, EF = 4, then the ratio of segment AD to AB is equal to (). Conventional method see article (1), pure geometric calculation method. AD · AD AB · AD = AD2AB · AD, it is easy to find that the denominator AB · AD represents the rectangle ABCD