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# Previous test question

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396
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X3Y5 - XY4 + X2Y2

divided by XY

Jul 4, 2017

#1
+7347
+3

$$\frac{x^3y^5-xy^4+x^2y^2}{xy}\\~\\ =\frac{x^3y^5}{xy}-\frac{xy^4}{xy}+\frac{x^2y^2}{xy} \\~\\ =\frac{x\,\cdot\,x\,\cdot\,x\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y}{x\,\cdot\,y}-\frac{x\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y}{x\,\cdot\,y}+\frac{x\,\cdot\,x\,\cdot\,y\,\cdot\,y}{x\,\cdot\,y} \\~\\ =\frac{\not{x}\,\cdot\,x\,\cdot\,x\,\cdot\,\not{y}\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y}{\not{x}\,\cdot\,\not{y}}-\frac{\not{x}\,\cdot\,\not{y}\,\cdot\,y\,\cdot\,y\,\cdot\,y}{\not{x}\,\cdot\,\not{y}}+\frac{\not{x}\,\cdot\,x\,\cdot\,\not{y}\,\cdot\,y}{\not{x}\,\cdot\,\not{y}} \\~\\ =x\,\cdot\,x\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y-y\,\cdot\,y\,\cdot\,y+x\,\cdot\,y \\~\\ =x^2y^4-y^3+xy$$

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Jul 4, 2017

#1
+7347
+3

$$\frac{x^3y^5-xy^4+x^2y^2}{xy}\\~\\ =\frac{x^3y^5}{xy}-\frac{xy^4}{xy}+\frac{x^2y^2}{xy} \\~\\ =\frac{x\,\cdot\,x\,\cdot\,x\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y}{x\,\cdot\,y}-\frac{x\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y}{x\,\cdot\,y}+\frac{x\,\cdot\,x\,\cdot\,y\,\cdot\,y}{x\,\cdot\,y} \\~\\ =\frac{\not{x}\,\cdot\,x\,\cdot\,x\,\cdot\,\not{y}\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y}{\not{x}\,\cdot\,\not{y}}-\frac{\not{x}\,\cdot\,\not{y}\,\cdot\,y\,\cdot\,y\,\cdot\,y}{\not{x}\,\cdot\,\not{y}}+\frac{\not{x}\,\cdot\,x\,\cdot\,\not{y}\,\cdot\,y}{\not{x}\,\cdot\,\not{y}} \\~\\ =x\,\cdot\,x\,\cdot\,y\,\cdot\,y\,\cdot\,y\,\cdot\,y-y\,\cdot\,y\,\cdot\,y+x\,\cdot\,y \\~\\ =x^2y^4-y^3+xy$$

hectictar Jul 4, 2017
#2
+2

y(x2y3 - y2 + x)

Jul 5, 2017