( x2x^{2} + xy + y2y^{2} ) / x3x^{3}-y3y^{3}

asked by guest
on Mar 25, 2025 at 6:33 am



You asked:

Evaluate the expression: x2+xy+y2x3−y3\frac{{x}^{2} + x y + {y}^{2}}{{x}^{3}} - {y}^{3}

MathBot Answer:

Evaluated



x2+xy+y2x3−y3=−y3+x2+xy+y2x3\displaystyle \frac{{x}^{2} + x y + {y}^{2}}{{x}^{3}} - {y}^{3} = - y^{3} + \frac{x^{2} + x y + y^{2}}{x^{3}}

Expanded

x2+xy+y2x3−y3=−y3+1x+yx2+y2x3\frac{{x}^{2} + x y + {y}^{2}}{{x}^{3}} - {y}^{3} = - y^{3} + \frac{1}{x} + \frac{y}{x^{2}} + \frac{y^{2}}{x^{3}}

Factored

x2+xy+y2x3−y3=−x3y3−x2−xy−y2x3\frac{{x}^{2} + x y + {y}^{2}}{{x}^{3}} - {y}^{3} = - \frac{x^{3} y^{3} - x^{2} - x y - y^{2}}{x^{3}}

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