Question

x+1/x-1 - x^2/（x+2）（x+1） 计算

x+1/x-1 - x^2/（x+2）（x+1） x+y/2x-2y - x^2+y^2/x^2-y^2
x+y/2x-2y - x²+y²/x²-y² x+1/x-1 - x²/（x+2）（x+1）

Answer 1

1、(x+1)/(x-1)-x²/(x+2)(x+1)
=[(x+1)(x+1)(x+2)-x²(x-1)]/(x-1)(x+1)(x+2)
=[(x²+2x+1)(x+2)-x^3+x²]/[(x-1)(x+2)(x+1)]
=[x^3+2x²+x+2x²+4x+2-x^3+x²]/[(x-1)(x+1)(x+2)]
=[5x²+5x+2]/[(x²-1)(x+2)
=(5x²+5x+2)/(x^3+2x²-x-2)
2、(x+y)/(2x+2y)-(x²+y²)/(x²-y²)
=1/2-(x²+y²)/(x²-y²)
=(x²-y²-2x²-2y²)/2(x²-y²)
=(-x²-3y²)/2(x²-y²)
3、(x+y)/(2x-2y)-(x²+y²)/(x²-y²)
=(x+y)/2(x-y)-(x²+y²)/(x+y)(x-y)
=[(x+y)(x+y)-2(x²+y²)]/[2(x+y)(x-y)]
=(x²+2xy+y²-2x²-2y²]/[2(x+y)(x-y)]
=-(x²-2xy+y²)/[2(x+y)(x-y)]
=-(x-y)²/[2(x+y)(x-y)]
=(y-x)/2(x+y)