(2x^5-4x^3-6x)/(x^2+1)^2
You asked:
Evaluate the expression: \(\frac{2 \cdot {x}^{5} - 4 \cdot {x}^{3} - 6 x}{{\left( {x}^{2} + 1 \right)}^{2}}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{2 \cdot {x}^{5} - 4 \cdot {x}^{3} - 6 x}{{\left( {x}^{2} + 1 \right)}^{2}} = \frac{2 x^{5} - 4 x^{3} - 6 x}{\left(x^{2} + 1\right)^{2}} \)
Expanded
\[\frac{2 \cdot {x}^{5} - 4 \cdot {x}^{3} - 6 x}{{\left( {x}^{2} + 1 \right)}^{2}} = \frac{2 x^{5}}{x^{4} + 2 x^{2} + 1} - \frac{4 x^{3}}{x^{4} + 2 x^{2} + 1} - \frac{6 x}{x^{4} + 2 x^{2} + 1}\]
Factored
\[\frac{2 \cdot {x}^{5} - 4 \cdot {x}^{3} - 6 x}{{\left( {x}^{2} + 1 \right)}^{2}} = \frac{2 x \left(x^{2} - 3\right)}{x^{2} + 1}\]