Finite Math Examples

$y = \frac{2}{1 + x}$

Step 1

Rewrite the equation as $\frac{2}{1 + x} = y$ .

$\frac{2}{1 + x} = y$

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.

$1 + x, 1$

Step 2.2

Remove parentheses.

$1 + x, 1$

Step 2.3

The LCM of one and any expression is the expression.

$1 + x$

Step 3

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

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Step 3.1

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

$\frac{2}{1 + x} (1 + x) = y (1 + x)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $1 + x$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2}{1 + x} (1 + x) = y (1 + x)$

Step 3.2.1.2

Rewrite the expression.

$2 = y (1 + x)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$2 = y \cdot 1 + y x$

Step 3.3.2

Multiply $y$ by $1$ .

$2 = y + y x$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $y + y x = 2$ .

$y + y x = 2$

Step 4.2

Subtract $y$ from both sides of the equation.

$y x = 2 - y$

Step 4.3

Divide each term in $y x = 2 - y$ by $y$ and simplify.

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Step 4.3.1

Divide each term in $y x = 2 - y$ by $y$ .

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

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $y$ .

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Step 4.3.2.1.1

Cancel the common factor.

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

Step 4.3.2.1.2

Divide $x$ by $1$ .

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

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Cancel the common factor of $y$ .

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Step 4.3.3.1.1

Cancel the common factor.

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

Step 4.3.3.1.2

Divide $- 1$ by $1$ .

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