Finite Math Examples

$\frac{x + y}{x - y} = \frac{- 4}{2}$

Step 1

Divide $- 4$ by $2$ .

$\frac{x + y}{x - y} = - 2$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$x - y, 1$

Step 2.2

Remove parentheses.

$x - y, 1$

Step 2.3

The LCM of one and any expression is the expression.

$x - y$

Step 3

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

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $x - y$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Rewrite the expression.

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

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

Step 3.3.2

Multiply $- 1$ by $- 2$ .

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

Step 4

Solve the equation.

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Step 4.1

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

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Step 4.1.1

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

$x + y + 2 x = 2 y$

Step 4.1.2

Add $x$ and $2 x$ .

$3 x + y = 2 y$

Step 4.2

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

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Step 4.2.1

Subtract $y$ from both sides of the equation.

$3 x = 2 y - y$

Step 4.2.2

Subtract $y$ from $2 y$ .

$3 x = y$

Step 4.3

Divide each term in $3 x = y$ by $3$ and simplify.

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Step 4.3.1

Divide each term in $3 x = y$ by $3$ .

$\frac{3 x}{3} = \frac{y}{3}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $3$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{y}{3}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{y}{3}$