Finite Math Examples

$a - a z = 2 z$

Step 1

Subtract $2 z$ from both sides of the equation.

$a - a z - 2 z = 0$

Step 2

Subtract $a$ from both sides of the equation.

$- a z - 2 z = - a$

Step 3

Factor $z$ out of $- a z - 2 z$ .

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Step 3.1

Factor $z$ out of $- a z$ .

$z (- a) - 2 z = - a$

Step 3.2

Factor $z$ out of $- 2 z$ .

$z (- a) + z \cdot - 2 = - a$

Step 3.3

Factor $z$ out of $z (- a) + z \cdot - 2$ .

$z (- a - 2) = - a$

Step 4

Divide each term in $z (- a - 2) = - a$ by $- a - 2$ and simplify.

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Step 4.1

Divide each term in $z (- a - 2) = - a$ by $- a - 2$ .

$\frac{z (- a - 2)}{- a - 2} = \frac{- a}{- a - 2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- a - 2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{z (- a - 2)}{- a - 2} = \frac{- a}{- a - 2}$

Step 4.2.1.2

Divide $z$ by $1$ .

$z = \frac{- a}{- a - 2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$z = - \frac{a}{- a - 2}$

Step 4.3.2

Factor $- 1$ out of $- a$ .

$z = - \frac{a}{- (a) - 2}$

Step 4.3.3

Rewrite $- 2$ as $- 1 (2)$ .

$z = - \frac{a}{- (a) - 1 (2)}$

Step 4.3.4

Factor $- 1$ out of $- (a) - 1 (2)$ .

$z = - \frac{a}{- (a + 2)}$

Step 4.3.5

Simplify the expression.

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Step 4.3.5.1

Rewrite $- (a + 2)$ as $- 1 (a + 2)$ .

$z = - \frac{a}{- 1 (a + 2)}$

Step 4.3.5.2

Move the negative in front of the fraction.

$z = - - \frac{a}{a + 2}$

Step 4.3.5.3

Multiply $- 1$ by $- 1$ .

$z = 1 \frac{a}{a + 2}$

Step 4.3.5.4

Multiply $\frac{a}{a + 2}$ by $1$ .

$z = \frac{a}{a + 2}$