Solve -1/x(8-1/x)

$$- \frac { 1 } { x } ( 8 - \frac { 1 } { x } )$$

Evaluate

$$\frac{1-8x}{x^{2}}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 8 times \frac{x}{x}.

$$\left(-\frac{1}{x}\right)\left(\frac{8x}{x}-\frac{1}{x}\right)$$

Since \frac{8x}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

$$\left(-\frac{1}{x}\right)\times \frac{8x-1}{x}$$

Multiply -\frac{1}{x} times \frac{8x-1}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(8x-1\right)}{xx}$$

Multiply x and x to get x^{2}.

$$\frac{-\left(8x-1\right)}{x^{2}}$$

To find the opposite of 8x-1, find the opposite of each term.

$$\frac{-8x-\left(-1\right)}{x^{2}}$$

The opposite of -1 is 1.

$$\frac{-8x+1}{x^{2}}$$

Expand

$$\frac{1-8x}{x^{2}}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 8 times \frac{x}{x}.

$$\left(-\frac{1}{x}\right)\left(\frac{8x}{x}-\frac{1}{x}\right)$$

Since \frac{8x}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

$$\left(-\frac{1}{x}\right)\times \frac{8x-1}{x}$$

Multiply -\frac{1}{x} times \frac{8x-1}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(8x-1\right)}{xx}$$

Multiply x and x to get x^{2}.

$$\frac{-\left(8x-1\right)}{x^{2}}$$

To find the opposite of 8x-1, find the opposite of each term.

$$\frac{-8x-\left(-1\right)}{x^{2}}$$

The opposite of -1 is 1.

$$\frac{-8x+1}{x^{2}}$$