(1)4y^2-x^2/-x^2+4xy-4y^2 (2)x^2y(5y^2-5x^2)/xy(10x^2-10xy) (3)a^2+b^2-c^2+2ab/a^2-b^2+c^2+2ac (4)x^

题目

(1)4y^2-x^2/-x^2+4xy-4y^2 (2)x^2y(5y^2-5x^2)/xy(10x^2-10xy) (3)a^2+b^2-c^2+2ab/a^2-b^2+c^2+2ac (4)x^n(a-1)^2n/x^2n(a-1)^n+1

答案

1、4y²-x²/-x²+4xy-4y²
=(2y+x)(2y-x)/-(x-2y)²
=-(2y+x)(x-2y)/-(x-2y)²
=2y+x / x-2y
2、x²y(5y²-5x²) / xy(10x²-10xy)
=x·5(y-x)(y+x) / 10x(x-y)
=-(x+y) / 2
3、a²+b²-c²+2ab / a²-b²+c²+2ac
=(a+b)²-c² / (a+c)²-b²
=(a+b+c)(a+b-c)/(a+c+b)(a+c-b)
=a+b-c / a-b+c
4、x^n(a-1)^2n / x^2n(a-1)^n+1
=x^n (a-1)^n (a-1)^n / x^n x^n (a-1)^n (a-1)
=(a-1)^n / x^n (a-1)
=(a-1)^(n-1) / x^n