Solve 1/x+4/frac{1{-8}}

$$\frac { \frac { 1 } { x } + 4 } { \frac { 1 } { - 8 } }$$

Evaluate

$$-32-\frac{8}{x}$$

Short Solution Steps

Divide \frac{1}{x}+4 by \frac{1}{-8} by multiplying \frac{1}{x}+4 by the reciprocal of \frac{1}{-8}.

$$\left(\frac{1}{x}+4\right)\left(-8\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x}{x}.

$$\left(\frac{1}{x}+\frac{4x}{x}\right)\left(-8\right)$$

Since \frac{1}{x} and \frac{4x}{x} have the same denominator, add them by adding their numerators.

$$\frac{1+4x}{x}\left(-8\right)$$

Express \frac{1+4x}{x}\left(-8\right) as a single fraction.

$$\frac{-\left(1+4x\right)\times 8}{x}$$

Multiply -1 and 8 to get -8.

$$\frac{-8\left(1+4x\right)}{x}$$

Use the distributive property to multiply -8 by 1+4x.

$$\frac{-8-32x}{x}$$

Expand

$$-32-\frac{8}{x}$$

Short Solution Steps

Divide \frac{1}{x}+4 by \frac{1}{-8} by multiplying \frac{1}{x}+4 by the reciprocal of \frac{1}{-8}.

$$\left(\frac{1}{x}+4\right)\left(-8\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x}{x}.

$$\left(\frac{1}{x}+\frac{4x}{x}\right)\left(-8\right)$$

Since \frac{1}{x} and \frac{4x}{x} have the same denominator, add them by adding their numerators.

$$\frac{1+4x}{x}\left(-8\right)$$

Express \frac{1+4x}{x}\left(-8\right) as a single fraction.

$$\frac{-\left(1+4x\right)\times 8}{x}$$

Multiply -1 and 8 to get -8.

$$\frac{-8\left(1+4x\right)}{x}$$

Use the distributive property to multiply -8 by 1+4x.

$$\frac{-8-32x}{x}$$