计算[2x/(x-1)-3x/(x+1)]÷x/x^2-1分解因式：x^3y-xy^3x^2-16x+64

更新时间：2022-06-10 10:17:55 95次访问

[2x/(x-1)-3x/(x+1)]÷x/(x²-1)

=[2/(x-1)-3/(x+1)]*(x²-1)

=2(x+1)-3(x-1)

=-x+5

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x³y-xy³

=xy(x²-y²)

=xy(x-y)(x+y)

//

x²-16x+64

=x²-2*8x+8²

=(x-8)²

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计算

原式

=(x-1)(x+1)(x²-1)(x^4+1)

=(x²-1)(x²-1)(x^4+1)

=(x^4-2x²+1)(x^4+1)

=(x^4+1)²-2x²(x^4+1)

=x^8+2x^4+1-2x^6-2x^4

=x^8-2x^6+1

因式分解

(x+3)(x+7)+25

=x²+10x+21+25

=x²+10x+46

不能在实数系数分解

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xⁿ=2，yⁿ=3

(x²y)²ⁿ

=(x²ⁿyⁿ)²

=[(xⁿ)²y]²

=(2²*3)²

=12²

=144