Question

先化简,后求值:x-y/x+3y - x^2-9y^2/x^2+6xy+9y^2 + 2y/x+3y,其中x=2,y=-

Answer 1

原式=(x-y)/(x+3y)-(x²-9y²)/(x²+6xy+9y²)+2y/(x+3y)

=(x-y)/(x+3y)-[(x+3y)(x-3y)/(x+3y)²]+2y/(x+3y)

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

=[(x-y)-(x-3y)+2y]/(x+3y)

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

=4y/(x+3y)

当x=2, y=-3时

原式=[4×(-3)]/[2+3×(-3)]

=-12/(-7)

=12/7