Basic Math Examples

$\frac{y - 1}{y} = 10$

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.

$y, 1$

Step 1.2

The LCM of one and any expression is the expression.

$y$

Step 2

Multiply each term in $\frac{y - 1}{y} = 10$ by $y$ to eliminate the fractions.

Tap for more steps...

Step 2.1

Multiply each term in $\frac{y - 1}{y} = 10$ by $y$ .

$\frac{y - 1}{y} y = 10 y$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $y$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{y - 1}{y} y = 10 y$

Step 2.2.1.2

Rewrite the expression.

$y - 1 = 10 y$

Step 3

Solve the equation.

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Subtract $10 y$ from both sides of the equation.

$y - 1 - 10 y = 0$

Step 3.1.2

Subtract $10 y$ from $y$ .

$- 9 y - 1 = 0$

Step 3.2

Add $1$ to both sides of the equation.

$- 9 y = 1$

Step 3.3

Divide each term in $- 9 y = 1$ by $- 9$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $- 9 y = 1$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{1}{- 9}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $- 9$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{1}{- 9}$

Step 3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{1}{- 9}$

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.

$y = - \frac{1}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{1}{9}$

Decimal Form:

$y = - 0.\overline{1}$