x+3y+9y^2/(x-3y)+6x^2y/(9y^2-x^2)
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x+3y+9y^2/(x-3y)+6x^2y/(9y^2-x^2)
x+3y+9y^2/(x-3y)+6x^2y/(9y^2-x^2)
=[(x+3y)(x-3y)+9y²]/(x-3y) + 6x²y/(9y²-x²)
=x²/(x-3y) + 6x²y/(9y²-x²)
=-x²/(3y-x) + 6x²y/[(3y+x)(3y-x)]
=[-x²(3y+x) + 6x²y]/[(3y+x)(3y-x)]
=x²(-3y-x+6y)/[(3y+x)(3y-x)]
=x²(-x+3y)/[(3y+x)(3y-x)]
=x²/(3y-x)
=[(x+3y)(x-3y)+9y²]/(x-3y) + 6x²y/(9y²-x²)
=x²/(x-3y) + 6x²y/(9y²-x²)
=-x²/(3y-x) + 6x²y/[(3y+x)(3y-x)]
=[-x²(3y+x) + 6x²y]/[(3y+x)(3y-x)]
=x²(-3y-x+6y)/[(3y+x)(3y-x)]
=x²(-x+3y)/[(3y+x)(3y-x)]
=x²/(3y-x)
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