(x-y)^-6/(y-x)^-4

asked by guest
on Feb 01, 2025 at 3:09 am



You asked:

Evaluate the expression: (x−y)−6(y−x)−4\frac{{\left( x - y \right)}^{-6}}{{\left( y - x \right)}^{-4}}

MathBot Answer:

Evaluated



(x−y)−6(y−x)−4=(−x+y)4(x−y)6\displaystyle \frac{{\left( x - y \right)}^{-6}}{{\left( y - x \right)}^{-4}} = \frac{\left(- x + y\right)^{4}}{\left(x - y\right)^{6}}

Expanded

(x−y)−6(y−x)−4=x4x6−6x5y+15x4y2−20x3y3+15x2y4−6y5x+y6−4x3yx6−6x5y+15x4y2−20x3y3+15x2y4−6y5x+y6+6x2y2x6−6x5y+15x4y2−20x3y3+15x2y4−6y5x+y6−4y3xx6−6x5y+15x4y2−20x3y3+15x2y4−6y5x+y6+y4x6−6x5y+15x4y2−20x3y3+15x2y4−6y5x+y6\frac{{\left( x - y \right)}^{-6}}{{\left( y - x \right)}^{-4}} = \frac{x^{4}}{x^{6} - 6 x^{5} y + 15 x^{4} y^{2} - 20 x^{3} y^{3} + 15 x^{2} y^{4} - 6 y^{5} x + y^{6}} - \frac{4 x^{3} y}{x^{6} - 6 x^{5} y + 15 x^{4} y^{2} - 20 x^{3} y^{3} + 15 x^{2} y^{4} - 6 y^{5} x + y^{6}} + \frac{6 x^{2} y^{2}}{x^{6} - 6 x^{5} y + 15 x^{4} y^{2} - 20 x^{3} y^{3} + 15 x^{2} y^{4} - 6 y^{5} x + y^{6}} - \frac{4 y^{3} x}{x^{6} - 6 x^{5} y + 15 x^{4} y^{2} - 20 x^{3} y^{3} + 15 x^{2} y^{4} - 6 y^{5} x + y^{6}} + \frac{y^{4}}{x^{6} - 6 x^{5} y + 15 x^{4} y^{2} - 20 x^{3} y^{3} + 15 x^{2} y^{4} - 6 y^{5} x + y^{6}}

Factored

(x−y)−6(y−x)−4=1(x−y)2\frac{{\left( x - y \right)}^{-6}}{{\left( y - x \right)}^{-4}} = \frac{1}{\left(x - y\right)^{2}}

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