Solve x^3+2x^2+x/(x+1)^2

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

Evaluate

$$x$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{x\left(x+1\right)^{2}}{\left(x+1\right)^{2}}$$

Cancel out \left(x+1\right)^{2} in both numerator and denominator.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Factor the expressions that are not already factored in \frac{x^{3}+2x^{2}+x}{\left(x+1\right)^{2}}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\left(x+1\right)^{2}}{\left(x+1\right)^{2}})$$

Cancel out \left(x+1\right)^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x)$$

The derivative of ax^{n} is nax^{n-1}.

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

For any term t except 0, t^{0}=1.

$$1$$