Finite Math Examples

$\frac{x - \frac{1}{5}}{x} - 1 = 4$

Step 1

Subtract $4$ from both sides of the equation.

$\frac{x - \frac{1}{5}}{x} - 1 - 4 = 0$

Step 2

Simplify $\frac{x - \frac{1}{5}}{x} - 1 - 4$ .

Tap for more steps...

Step 2.1

Find the common denominator.

Tap for more steps...

Step 2.1.1

Write $- 1$ as a fraction with denominator $1$ .

$\frac{x - \frac{1}{5}}{x} + \frac{- 1}{1} - 4 = 0$

Step 2.1.2

Multiply $\frac{- 1}{1}$ by $\frac{x}{x}$ .

$\frac{x - \frac{1}{5}}{x} + \frac{- 1}{1} \cdot \frac{x}{x} - 4 = 0$

Step 2.1.3

Multiply $\frac{- 1}{1}$ by $\frac{x}{x}$ .

$\frac{x - \frac{1}{5}}{x} + \frac{- x}{x} - 4 = 0$

Step 2.1.4

Write $- 4$ as a fraction with denominator $1$ .

$\frac{x - \frac{1}{5}}{x} + \frac{- x}{x} + \frac{- 4}{1} = 0$

Step 2.1.5

Multiply $\frac{- 4}{1}$ by $\frac{x}{x}$ .

$\frac{x - \frac{1}{5}}{x} + \frac{- x}{x} + \frac{- 4}{1} \cdot \frac{x}{x} = 0$

Step 2.1.6

Multiply $\frac{- 4}{1}$ by $\frac{x}{x}$ .

$\frac{x - \frac{1}{5}}{x} + \frac{- x}{x} + \frac{- 4 x}{x} = 0$

Step 2.2

Combine the numerators over the common denominator.

$\frac{x - \frac{1}{5} - x - 4 x}{x} = 0$

Step 2.3

Combine the opposite terms in $x - \frac{1}{5} - x - 4 x$ .

Tap for more steps...

Step 2.3.1

Subtract $x$ from $x$ .

$\frac{0 - \frac{1}{5} - 4 x}{x} = 0$

Step 2.3.2

Subtract $\frac{1}{5}$ from $0$ .

$\frac{- \frac{1}{5} - 4 x}{x} = 0$

Step 2.4

Simplify the numerator.

Tap for more steps...

Step 2.4.1

To write $- 4 x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{- \frac{1}{5} - 4 x \cdot \frac{5}{5}}{x} = 0$

Step 2.4.2

Combine $- 4 x$ and $\frac{5}{5}$ .

$\frac{- \frac{1}{5} + \frac{- 4 x \cdot 5}{5}}{x} = 0$

Step 2.4.3

Combine the numerators over the common denominator.

$\frac{\frac{- 1 - 4 x \cdot 5}{5}}{x} = 0$

Step 2.4.4

Multiply $5$ by $- 4$ .

$\frac{\frac{- 1 - 20 x}{5}}{x} = 0$

Step 2.5

Multiply the numerator by the reciprocal of the denominator.

$\frac{- 1 - 20 x}{5} \cdot \frac{1}{x} = 0$

Step 2.6

Multiply $\frac{- 1 - 20 x}{5}$ by $\frac{1}{x}$ .

$\frac{- 1 - 20 x}{5 x} = 0$

Step 2.7

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{- 1 (1) - 20 x}{5 x} = 0$

Step 2.8

Factor $- 1$ out of $- 20 x$ .

$\frac{- 1 (1) - (20 x)}{5 x} = 0$

Step 2.9

Factor $- 1$ out of $- 1 (1) - (20 x)$ .

$\frac{- 1 (1 + 20 x)}{5 x} = 0$

Step 2.10

Move the negative in front of the fraction.

$- \frac{1 + 20 x}{5 x} = 0$

Step 3

Set the numerator equal to zero.

$1 + 20 x = 0$

Step 4

Solve the equation for $x$ .

Tap for more steps...

Step 4.1

Subtract $1$ from both sides of the equation.

$20 x = - 1$

Step 4.2

Divide each term in $20 x = - 1$ by $20$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $20 x = - 1$ by $20$ .

$\frac{20 x}{20} = \frac{- 1}{20}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $20$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{20 x}{20} = \frac{- 1}{20}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{20}$

Step 4.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.3.1

Move the negative in front of the fraction.

$x = - \frac{1}{20}$