Question

已知P=(x-y分之x^2)-(x-y分之y^2),Q=x-y+2y²/x+y当x=2,y=-1时比较P、Q值的大小.

Answer 1

P=x²/(x-y)-y²/(x-y)=(x²-y²)/(x-y)=(x+y)(x-y)/(x-y)=x+y

Q=x-y +2y²/(x+y)=[(x-y)(x+y)+2y²]/(x+y)=(x²-y²+2y²)/(x+y)=(x²+y²)/(x+y)

P-Q=x+y -(x²+y²)/(x+y)

=[(x+y)²-(x²+y²)]/(x+y)

=(x²+2xy+y²-x²-y²)/(x+y)

=2xy/(x+y)

x=2 y=-1代入

P-Q=2×2×(-1)/[2+(-1)]=-4