Question

数学高手来

约分求值（题目全是分式，数字和字母不在一起平方或次方）
1、（1-4x的4次方）除以（2x的3次方+x）其中x=-2
2、（x的平方y-2xy+y）除以（y-x的平方y） 其中x=-2
3、（a的平方-3ab）除以（a的平方-6ab+9b的平方）其中a=2分之3，b=-3分之2

Answer 1

(1-4x^4)/(2x^3+x)
=[1^2-(2x^2)^2]/[x(2x^2+1)]
=[(1+2x^2)(1-2x^2)]/[x(2x^2+1)]
=(1-2x^2)/x
=(1-2×4)/(-2)
=(-7)/(-2)
=7/2

(x^2y-2xy+y)/(y-x^2y)
=[y(x^2-2x+1)]/[y(1-x^2)]
=[y(x-1)^2]/[y(1-x^2)]
=(x-1)^2/[(1-x^2)]
=[(-2-1)^2]/(1-4)
=9/(-3)
=-3

(a^2-3ab)/(a^2-6ab+9b^2)
=[a(a-3b)]/(a-3b)^2
=a/(a-3b)
=(3/2)/(3/2+2)
=(3/2)/(7/2)
=3/7

Answer 2

(1-4x^4)/(2x^3+x)=(1-4x(-2)^4)/(2x(-2)^3-2)=(1-4x16)/(-16-2)=-63/(-18)=7/2
(x²y-2xy+y)/(y-x²y)=(x²-2x+1)/(1-x²)=(x-1)²/(1+x)(1-x)=(1-x)/(1+x)=(1+2)/(1-2)=-3
(a²-3ab)/(a²-6ab+9b²)=a(a-3b)/(a-3b)²=a/(a-3b)=(3/2)/(3/2-3x(-2/3))=(3/2)/(3/2+2)=(3/2)/(7/2)=3/7

Answer 3

(1-4x^4)/(2x^3+x)=(1-4x(-2)^4)/(2x(-2)^3-2)=(1-4x16)/(-16-2)=-63/(-18)=7/2
(x²y-2xy+y)/(y-x²y)=(x²-2x+1)/(1-x²)=(x-1)²/(1+x)(1-x)=(1-x)/(1+x)=(1+2)/(1-2)=-3