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=-
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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
=(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
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