Question

问一道初二相似图形，线段的比一道数学题，求过程讲解，要细致，好的加分，急

若三分之x=五分之y=七分之z，则x+y-z分之x-y+z=？

Answer 1

∵x/3=y/5=z/7 ∴x：y：z=3:5:7
设x=3k y=5k z=7k
则x-y+z/x+y-z=3k-5k+7k/3k+5k-7k=5k/k=5

Answer 2

令三分之x=五分之y=七分之z=t
则x=3t,y=5t,z=7t
(x-y+z)/(x+y-z)
=(3t-5t+7t)/(3t+5t-7t)
=(3-5+7)/(3+5-7)
=5

追问

看不懂，t是啥？

追答

连等式一般这样设，然后把x,y,z用t表示

Answer 3

(x-y+z)/(x+y-z)分子分母同时乘以3得到（x/3-y/3+z/3)/(x/3+y/3-z/3)
将x/3=y/5带入上式可以得到（y/5-y/3+z/3)/(y/5+y/3-z/3)
将上式分子分母都同分母化简得到【（5z-2y)/15]/[(8y-5z)/15]继续化简得到(5z-2y)/(8y-5z)(式子1）
又由y/5=z/7得到5z=7y
将5z=7y带入式子1可以得到（7y-zy）/(8y-7y)化简得到5y/y最后得到出等于5

Answer 4

设x／3=y／5＝z／7＝a
x=3a y=5a z=7a
﹙3a-5a+7a﹚／﹙3a﹢5a﹣7a﹚＝5a／a＝5