Pre-Algebra Examples

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

Step 1

Find the LCD of the terms in the equation.

Tap for more steps...

Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x, 1$

Step 1.2

The LCM of one and any expression is the expression.

$x$

Step 2

Multiply each term in $\frac{x - 1}{x} = 20$ by $x$ to eliminate the fractions.

Tap for more steps...

Step 2.1

Multiply each term in $\frac{x - 1}{x} = 20$ by $x$ .

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

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $x$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Rewrite the expression.

$x - 1 = 20 x$

Step 3

Solve the equation.

Tap for more steps...

Step 3.1

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 3.1.1

Subtract $20 x$ from both sides of the equation.

$x - 1 - 20 x = 0$

Step 3.1.2

Subtract $20 x$ from $x$ .

$- 19 x - 1 = 0$

Step 3.2

Add $1$ to both sides of the equation.

$- 19 x = 1$

Step 3.3

Divide each term in $- 19 x = 1$ by $- 19$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $- 19 x = 1$ by $- 19$ .

$\frac{- 19 x}{- 19} = \frac{1}{- 19}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $- 19$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 19 x}{- 19} = \frac{1}{- 19}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{- 19}$

Step 3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.1

Move the negative in front of the fraction.

$x = - \frac{1}{19}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{19}$

Decimal Form:

$x = - 0.05263157 \dots$