Finite Math Examples

$\frac{3 x - 2 y}{2 x - 3 y} = \frac{6}{- 6}$

Step 1

Divide $6$ by $- 6$ .

$\frac{3 x - 2 y}{2 x - 3 y} = - 1$

Step 2

Find the LCD of the terms in the equation.

Tap for more steps...

Step 2.1

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

$2 x - 3 y, 1$

Step 2.2

Remove parentheses.

$2 x - 3 y, 1$

Step 2.3

The LCM of one and any expression is the expression.

$2 x - 3 y$

Step 3

Multiply each term in $\frac{3 x - 2 y}{2 x - 3 y} = - 1$ by $2 x - 3 y$ to eliminate the fractions.

Tap for more steps...

Step 3.1

Multiply each term in $\frac{3 x - 2 y}{2 x - 3 y} = - 1$ by $2 x - 3 y$ .

$\frac{3 x - 2 y}{2 x - 3 y} (2 x - 3 y) = - (2 x - 3 y)$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $2 x - 3 y$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{3 x - 2 y}{2 x - 3 y} (2 x - 3 y) = - (2 x - 3 y)$

Step 3.2.1.2

Rewrite the expression.

$3 x - 2 y = - (2 x - 3 y)$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Apply the distributive property.

$3 x - 2 y = - (2 x) - (- 3 y)$

Step 3.3.2

Multiply.

Tap for more steps...

Step 3.3.2.1

Multiply $2$ by $- 1$ .

$3 x - 2 y = - 2 x - (- 3 y)$

Step 3.3.2.2

Multiply $- 3$ by $- 1$ .

$3 x - 2 y = - 2 x + 3 y$

Step 4

Solve the equation.

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Add $2 x$ to both sides of the equation.

$3 x - 2 y + 2 x = 3 y$

Step 4.1.2

Add $3 x$ and $2 x$ .

$5 x - 2 y = 3 y$

Step 4.2

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 4.2.1

Add $2 y$ to both sides of the equation.

$5 x = 3 y + 2 y$

Step 4.2.2

Add $3 y$ and $2 y$ .

$5 x = 5 y$

Step 4.3

Divide each term in $5 x = 5 y$ by $5$ and simplify.

Tap for more steps...

Step 4.3.1

Divide each term in $5 x = 5 y$ by $5$ .

$\frac{5 x}{5} = \frac{5 y}{5}$

Step 4.3.2

Simplify the left side.

Tap for more steps...

Step 4.3.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 4.3.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{5 y}{5}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{5 y}{5}$

Step 4.3.3

Simplify the right side.

Tap for more steps...

Step 4.3.3.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 4.3.3.1.1

Cancel the common factor.

$x = \frac{5 y}{5}$

Step 4.3.3.1.2

Divide $y$ by $1$ .

$x = y$