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X3Y5 - XY4 + X2Y2 

divided by XY

Guest Jul 4, 2017

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 #1
avatar+4777 
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\(\frac{x^3y^5-xy^4+x^2y^2}{xy}\\~\\ =\frac{x^3y^5}{xy}-\frac{xy^4}{xy}+\frac{x^2y^2}{xy} \\~\\ =\frac{x\,\cdot\,x\,\cdot\,x\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y}{x\,\cdot\,y}-\frac{x\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y}{x\,\cdot\,y}+\frac{x\,\cdot\,x\,\cdot\,y\,\cdot\,y}{x\,\cdot\,y} \\~\\ =\frac{\not{x}\,\cdot\,x\,\cdot\,x\,\cdot\,\not{y}\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y}{\not{x}\,\cdot\,\not{y}}-\frac{\not{x}\,\cdot\,\not{y}\,\cdot\,y\,\cdot\,y\,\cdot\,y}{\not{x}\,\cdot\,\not{y}}+\frac{\not{x}\,\cdot\,x\,\cdot\,\not{y}\,\cdot\,y}{\not{x}\,\cdot\,\not{y}} \\~\\ =x\,\cdot\,x\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y-y\,\cdot\,y\,\cdot\,y+x\,\cdot\,y \\~\\ =x^2y^4-y^3+xy\)

hectictar  Jul 4, 2017
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 #1
avatar+4777 
+3
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\(\frac{x^3y^5-xy^4+x^2y^2}{xy}\\~\\ =\frac{x^3y^5}{xy}-\frac{xy^4}{xy}+\frac{x^2y^2}{xy} \\~\\ =\frac{x\,\cdot\,x\,\cdot\,x\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y}{x\,\cdot\,y}-\frac{x\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y}{x\,\cdot\,y}+\frac{x\,\cdot\,x\,\cdot\,y\,\cdot\,y}{x\,\cdot\,y} \\~\\ =\frac{\not{x}\,\cdot\,x\,\cdot\,x\,\cdot\,\not{y}\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y}{\not{x}\,\cdot\,\not{y}}-\frac{\not{x}\,\cdot\,\not{y}\,\cdot\,y\,\cdot\,y\,\cdot\,y}{\not{x}\,\cdot\,\not{y}}+\frac{\not{x}\,\cdot\,x\,\cdot\,\not{y}\,\cdot\,y}{\not{x}\,\cdot\,\not{y}} \\~\\ =x\,\cdot\,x\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y-y\,\cdot\,y\,\cdot\,y+x\,\cdot\,y \\~\\ =x^2y^4-y^3+xy\)

hectictar  Jul 4, 2017
 #2
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y(x2y3 - y2 + x)

Guest Jul 5, 2017

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