Question

计算（1）2x^2-4x/x+2×x^2+2x/x^2-4x+4

计算（1）2x^2-4x/x+2·x^2+2x/x^2-4x+4
（2）x^2+2xy+y^2/x^2+xy÷1/x
（3）x^2+xy/x^2-xy÷(x+y)÷xy/y^2-xy
（4）2x-6/x^2-4x+4÷(x+3)·x-2/x-3

Answer 1

（1）2x^2-4x/x+2·x^2+2x/x^2-4x+4
=2x(x-2)/(x+2) · x(x+2)/(x-2)²
=2x²/(x-2)

（2）x^2+2xy+y^2/x^2+xy÷1/x
=(x+y)²/x(x+y) · x
=x+y

（3）x^2+xy/x^2-xy÷(x+y)÷xy/y^2-xy
=x(x+y)/x(x-y) · 1/(x+y) · y(y-x)/xy
=-1/x

（4）2x-6/x^2-4x+4÷(x+3)·x-2/x-3
=2(x-3)/(x-2)² · 1/(x+3) · (x-2)/(x-3)
=2/(x-2)(x+3)
=2/(x²+x-6)