Question

分式的加减

1.2x^2/x-y -x^2-4xy +2y^2-x^2/x-y
2.3/2x+4 -6/4-x^2 +9/2x-4

Answer 1

1.2x^2/x-y -x^2-4xy/y-x +2y^2-x^2/x-y
=2x²/(x-y)+(x²-4xy)/(x-y)+(2y²-x²)/(x-y)
=(2x²+x²-4xy+2y²-x²)/(x-y)
=(2x²-4xy+2y²)/(x-y)
=2(x-y)²/(x-y)
=2x-2y

2.3/2x+4 -6/4-x^2 +9/2x-4
=3[2(x+2)]+6/(x+2)(x-2)+9/[2(x-2)]
=[3(x-2)+12+9(x+2)]/[2(x+2)(x-2)]
=(3x-6+12+9x+18)/[2(x+2)(x-2)]
=(12x-24)/[2(x+2)(x-2)]
=12(x-2)/[2(x+2)(x-2)]
=6/(x+2)