Question

数学分式化简

化简y²-x²分之3x-3y+（x²-y²分之x²-2xy+y²）-（x+2分之x²-x-6）÷（x+y）

Answer 1

(y²-x²)分之(3x-3y)+(x²-y²)分之(x²-2xy+y²)-(x+2)分之(x²-x-6)÷(x+y)
=-[(x+y)(x-y)]分之[3(x-y)]+[(x+y)(x-y)]分之(x-y)²-(x+2)分之[(x+2)(x-3)]÷(x+y)
=-(x+y)分之3+(x+y)分之(x-y)-(x+y)分之(x-3)
=(x+y)分之[-3+(x-y)-(x-3)]
=(x+y)分之(-3+x-y-x+3)
=(x+y)分之(-y)
=-(x+y)分之y
慢慢化简，没有简便方法，一步步算也能得出正确答案

Answer 2

(y²-x²)分之(3x-3y)+(x²-y²)分之(x²-2xy+y²)-(x+2)分之(x²-x-6)÷(x+y)
=-[(x+y)(x-y)]分之[3(x-y)]+[(x+y)(x-y)]分之(x-y)²-(x+2)分之[(x+2)(x-3)]÷(x+y)
=-(x+y)分之3+(x+y)分之(x-y)-(x+y)分之(x-3)
=(x+y)分之[-3+(x-y)-(x-3)]
=(x+y)分之(-3+x-y-x+3)
=(x+y)分之(-y)
=-(x+y)分之y

Answer 3

Answer 4

y²-x²分之3x-3y+（x²-y²分之x²-2xy+y²）-（x+2分之x²-x-6）÷（x+y）
=-3/（x+y）+(x-y)/（x+y)-（x-3)/（x+y)
=（-3+x-y-x+3)/（x+y)
=-y/(x+y)

Answer 5

原式=3（x-y)/(y^2-x^2)+(x+y)(x-y)/(x-y)^2-(x-3)(x+2)/(x+2)/(x+y)
=(-3+x+y-x+3)/(x+y）
=y/(x+y)