Algebra Examples

$x = \frac{1}{9} \cdot \frac{1}{y}$

Step 1

Rewrite the equation as $\frac{1}{9} \cdot \frac{1}{y} = x$ .

$\frac{1}{9} \cdot \frac{1}{y} = x$

Step 2

Multiply both sides of the equation by $9$ .

$9 (\frac{1}{9} \cdot \frac{1}{y}) = 9 x$

Step 3

Simplify the left side.

Tap for more steps...

Step 3.1

Simplify $9 (\frac{1}{9} \cdot \frac{1}{y})$ .

Tap for more steps...

Step 3.1.1

Multiply $\frac{1}{9}$ by $\frac{1}{y}$ .

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

Step 3.1.2

Cancel the common factor of $9$ .

Tap for more steps...

Step 3.1.2.1

Factor $9$ out of $9 y$ .

$9 \frac{1}{9 (y)} = 9 x$

Step 3.1.2.2

Cancel the common factor.

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

Step 3.1.2.3

Rewrite the expression.

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

Step 4

Find the LCD of the terms in the equation.

Tap for more steps...

Step 4.1

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

$y, 1$

Step 4.2

The LCM of one and any expression is the expression.

$y$

Step 5

Multiply each term in $\frac{1}{y} = 9 x$ by $y$ to eliminate the fractions.

Tap for more steps...

Step 5.1

Multiply each term in $\frac{1}{y} = 9 x$ by $y$ .

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

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $y$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Rewrite the expression.

$1 = 9 x y$

Step 6

Solve the equation.

Tap for more steps...

Step 6.1

Rewrite the equation as $9 x y = 1$ .

$9 x y = 1$

Step 6.2

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

Tap for more steps...

Step 6.2.1

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

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

Step 6.2.2

Simplify the left side.

Tap for more steps...

Step 6.2.2.1

Cancel the common factor of $9$ .

Tap for more steps...

Step 6.2.2.1.1

Cancel the common factor.

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

Step 6.2.2.1.2

Rewrite the expression.

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

Step 6.2.2.2

Cancel the common factor of $x$ .

Tap for more steps...

Step 6.2.2.2.1

Cancel the common factor.

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

Step 6.2.2.2.2

Divide $y$ by $1$ .

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

Step 7

The given equation $y = \frac{1}{9 x}$ can not be written as $y = k x$ , so $y$ doesn't vary directly with $x$ .

$y$ doesn't vary directly with $x$