Algebra Examples

$a x + z = a w - y$

Step 1

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

$a x + z - a w = - y$

Step 2

Subtract $z$ from both sides of the equation.

$a x - a w = - y - z$

Step 3

Factor $a$ out of $a x - a w$ .

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Step 3.1

Factor $a$ out of $a x$ .

$a (x) - a w = - y - z$

Step 3.2

Factor $a$ out of $- a w$ .

$a (x) + a (- 1 w) = - y - z$

Step 3.3

Factor $a$ out of $a (x) + a (- 1 w)$ .

$a (x - 1 w) = - y - z$

Step 4

Rewrite $- 1 w$ as $- w$ .

$a (x - w) = - y - z$

Step 5

Divide each term in $a (x - w) = - y - z$ by $x - w$ and simplify.

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Step 5.1

Divide each term in $a (x - w) = - y - z$ by $x - w$ .

$\frac{a (x - w)}{x - w} = \frac{- y}{x - w} + \frac{- z}{x - w}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $x - w$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{a (x - w)}{x - w} = \frac{- y}{x - w} + \frac{- z}{x - w}$

Step 5.2.1.2

Divide $a$ by $1$ .

$a = \frac{- y}{x - w} + \frac{- z}{x - w}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Move the negative in front of the fraction.

$a = - \frac{y}{x - w} + \frac{- z}{x - w}$

Step 5.3.1.2

Move the negative in front of the fraction.

$a = - \frac{y}{x - w} - \frac{z}{x - w}$

Step 5.3.2

Simplify terms.

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Step 5.3.2.1

Combine the numerators over the common denominator.

$a = \frac{- y - z}{x - w}$

Step 5.3.2.2

Factor $- 1$ out of $- y$ .

$a = \frac{- (y) - z}{x - w}$

Step 5.3.2.3

Factor $- 1$ out of $- z$ .

$a = \frac{- (y) - (z)}{x - w}$

Step 5.3.2.4

Factor $- 1$ out of $- (y) - (z)$ .

$a = \frac{- (y + z)}{x - w}$

Step 5.3.2.5

Simplify the expression.

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Step 5.3.2.5.1

Rewrite $- (y + z)$ as $- 1 (y + z)$ .

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

Step 5.3.2.5.2

Move the negative in front of the fraction.

$a = - \frac{y + z}{x - w}$