Basic Math Examples

$w = \frac{z - 1}{z + 1}$

Step 1

Rewrite the equation as $\frac{z - 1}{z + 1} = w$ .

$\frac{z - 1}{z + 1} = w$

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.

$z + 1, 1$

Step 2.2

Remove parentheses.

$z + 1, 1$

Step 2.3

The LCM of one and any expression is the expression.

$z + 1$

Step 3

Multiply each term in $\frac{z - 1}{z + 1} = w$ by $z + 1$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{z - 1}{z + 1} = w$ by $z + 1$ .

$\frac{z - 1}{z + 1} (z + 1) = w (z + 1)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $z + 1$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{z - 1}{z + 1} (z + 1) = w (z + 1)$

Step 3.2.1.2

Rewrite the expression.

$z - 1 = w (z + 1)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$z - 1 = w z + w \cdot 1$

Step 3.3.2

Multiply $w$ by $1$ .

$z - 1 = w z + w$

Step 4

Solve the equation.

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Step 4.1

Subtract $w z$ from both sides of the equation.

$z - 1 - w z = w$

Step 4.2

Add $1$ to both sides of the equation.

$z - w z = w + 1$

Step 4.3

Factor $z$ out of $z - w z$ .

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Step 4.3.1

Factor $z$ out of $z^{1}$ .

$z \cdot 1 - w z = w + 1$

Step 4.3.2

Factor $z$ out of $- w z$ .

$z \cdot 1 + z (- w) = w + 1$

Step 4.3.3

Factor $z$ out of $z \cdot 1 + z (- w)$ .

$z (1 - w) = w + 1$

Step 4.4

Divide each term in $z (1 - w) = w + 1$ by $1 - w$ and simplify.

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Step 4.4.1

Divide each term in $z (1 - w) = w + 1$ by $1 - w$ .

$\frac{z (1 - w)}{1 - w} = \frac{w}{1 - w} + \frac{1}{1 - w}$

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $1 - w$ .

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Step 4.4.2.1.1

Cancel the common factor.

$\frac{z (1 - w)}{1 - w} = \frac{w}{1 - w} + \frac{1}{1 - w}$

Step 4.4.2.1.2

Divide $z$ by $1$ .

$z = \frac{w}{1 - w} + \frac{1}{1 - w}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Combine the numerators over the common denominator.

$z = \frac{w + 1}{1 - w}$