Solve f(x)=x^4-x^2/x^3-x

$$f ( x ) = \frac { x ^ { 4 } - x ^ { 2 } } { x ^ { 3 } - x }$$

Evaluate

$$x$$

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out x\left(x-1\right)\left(x+1\right) 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^{4}-x^{2}}{x^{3}-x}.

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

Cancel out x\left(x-1\right)\left(x+1\right) 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.

$$1$$