Solve x^2/x-5*x^2-x-20/x^2+4x

$$\frac { x ^ { 2 } } { x - 5 } \cdot \frac { x ^ { 2 } - x - 20 } { x ^ { 2 } + 4 x }$$

Evaluate

$$x$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-x-20}{x^{2}+4x}.

$$\frac{x^{2}}{x-5}\times \frac{\left(x-5\right)\left(x+4\right)}{x\left(x+4\right)}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{x^{2}}{x-5}\times \frac{x-5}{x}$$

Multiply \frac{x^{2}}{x-5} times \frac{x-5}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{2}\left(x-5\right)}{\left(x-5\right)x}$$

Cancel out x\left(x-5\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^{2}-x-20}{x^{2}+4x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}}{x-5}\times \frac{\left(x-5\right)\left(x+4\right)}{x\left(x+4\right)})$$

Cancel out x+4 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}}{x-5}\times \frac{x-5}{x})$$

Multiply \frac{x^{2}}{x-5} times \frac{x-5}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}\left(x-5\right)}{\left(x-5\right)x})$$

Cancel out x\left(x-5\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.

$$1$$