\frac{2x^3 + 2x^2 + 2}{(x + 1)^2(x^2 + 1)}

asked by guest
on Jan 12, 2025 at 9:55 pm



You asked:

Evaluate the expression: \(\frac{2 {x}^{3} + 2 {x}^{2} + 2}{{\left( x + 1 \right)}^{2} \left({x}^{2} + 1\right)}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{2 {x}^{3} + 2 {x}^{2} + 2}{{\left( x + 1 \right)}^{2} \left({x}^{2} + 1\right)} = \frac{2 x^{3} + 2 x^{2} + 2}{\left(x^{2} + 1\right) \left(x + 1\right)^{2}} \)

Expanded

\[\frac{2 {x}^{3} + 2 {x}^{2} + 2}{{\left( x + 1 \right)}^{2} \left({x}^{2} + 1\right)} = \frac{2 x^{3}}{x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 1} + \frac{2 x^{2}}{x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 1} + \frac{2}{x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 1}\]

Factored

\[\frac{2 {x}^{3} + 2 {x}^{2} + 2}{{\left( x + 1 \right)}^{2} \left({x}^{2} + 1\right)} = \frac{2 \left(x^{3} + x^{2} + 1\right)}{\left(x^{2} + 1\right) \left(x + 1\right)^{2}}\]

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