x3x25x+15(x+1)(x2)2\frac{x^{3} - x^{2} - 5x + 15}{(x + 1)(x - 2)^{2}}

asked by guest
on Jan 28, 2025 at 2:13 pm



You asked:

Evaluate the expression: x3x25x+15(x+1)(x2)2\frac{{x}^{3} - {x}^{2} - 5 x + 15}{\left(x + 1\right) {\left( x - 2 \right)}^{2}}

MathBot Answer:

Evaluated



x3x25x+15(x+1)(x2)2=x3x25x+15(x2)2(x+1)\displaystyle \frac{{x}^{3} - {x}^{2} - 5 x + 15}{\left(x + 1\right) {\left( x - 2 \right)}^{2}} = \frac{x^{3} - x^{2} - 5 x + 15}{\left(x - 2\right)^{2} \left(x + 1\right)}


Expanded

x3x25x+15(x+1)(x2)2=x3x33x2+4x2x33x2+45xx33x2+4+15x33x2+4\frac{{x}^{3} - {x}^{2} - 5 x + 15}{\left(x + 1\right) {\left( x - 2 \right)}^{2}} = \frac{x^{3}}{x^{3} - 3 x^{2} + 4} - \frac{x^{2}}{x^{3} - 3 x^{2} + 4} - \frac{5 x}{x^{3} - 3 x^{2} + 4} + \frac{15}{x^{3} - 3 x^{2} + 4}