Solve 18x^2/x-1/frac{x{2x-2}}

$$\frac { \frac { 18 x ^ { 2 } } { x - 1 } } { \frac { x } { 2 x - 2 } }$$

Evaluate

$$36x$$

Short Solution Steps

Divide \frac{18x^{2}}{x-1} by \frac{x}{2x-2} by multiplying \frac{18x^{2}}{x-1} by the reciprocal of \frac{x}{2x-2}.

$$\frac{18x^{2}\left(2x-2\right)}{\left(x-1\right)x}$$

Cancel out x in both numerator and denominator.

$$\frac{18x\left(2x-2\right)}{x-1}$$

Factor the expressions that are not already factored.

$$\frac{2\times 18x\left(x-1\right)}{x-1}$$

Cancel out x-1 in both numerator and denominator.

$$2\times 18x$$

Expand the expression.

$$36x$$

Differentiate w.r.t. x

$$36$$

Steps Using Definition of a Derivative

Divide \frac{18x^{2}}{x-1} by \frac{x}{2x-2} by multiplying \frac{18x^{2}}{x-1} by the reciprocal of \frac{x}{2x-2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{18x^{2}\left(2x-2\right)}{\left(x-1\right)x})$$

Cancel out x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{18x\left(2x-2\right)}{x-1})$$

Factor the expressions that are not already factored in \frac{18x\left(2x-2\right)}{x-1}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\times 18x\left(x-1\right)}{x-1})$$

Cancel out x-1 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2\times 18x)$$

Expand the expression.

$$\frac{\mathrm{d}}{\mathrm{d}x}(36x)$$

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

$$36x^{1-1}$$

Subtract 1 from 1.

$$36x^{0}$$

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

$$36\times 1$$

For any term t, t\times 1=t and 1t=t.

$$36$$