Algebra Examples

$\frac{b - a}{a - c} = \frac{x}{c - a}$

Step 1

Rewrite the equation as $\frac{x}{c - a} = \frac{b - a}{a - c}$ .

$\frac{x}{c - a} = \frac{b - a}{a - c}$

Step 2

Multiply both sides by $c - a$ .

$\frac{x}{c - a} (c - a) = \frac{b - a}{a - c} (c - a)$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $c - a$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{x}{c - a} (c - a) = \frac{b - a}{a - c} (c - a)$

Step 3.1.1.2

Rewrite the expression.

$x = \frac{b - a}{a - c} (c - a)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{b - a}{a - c} (c - a)$ .

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Step 3.2.1.1

Multiply $\frac{b - a}{a - c}$ by $c - a$ .

$x = \frac{(b - a) (c - a)}{a - c}$

Step 3.2.1.2

Cancel the common factor of $c - a$ and $a - c$ .

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Step 3.2.1.2.1

Factor $- 1$ out of $c$ .

$x = \frac{(b - a) (- 1 (- c) - a)}{a - c}$

Step 3.2.1.2.2

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

$x = \frac{(b - a) (- 1 (- c) - (a))}{a - c}$

Step 3.2.1.2.3

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

$x = \frac{(b - a) (- 1 (- c + a))}{a - c}$

Step 3.2.1.2.4

Reorder terms.

$x = \frac{(b - a) (- 1 (a - c))}{a - c}$

Step 3.2.1.2.5

Cancel the common factor.

$x = \frac{(b - a) (- 1 (a - c))}{a - c}$

Step 3.2.1.2.6

Divide $(b - a) \cdot (- 1)$ by $1$ .

$x = (b - a) \cdot (- 1)$

Step 3.2.1.3

Apply the distributive property.

$x = b \cdot - 1 - a \cdot - 1$

Step 3.2.1.4

Move $- 1$ to the left of $b$ .

$x = - 1 \cdot b - a \cdot - 1$

Step 3.2.1.5

Multiply $- a \cdot - 1$ .

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Step 3.2.1.5.1

Multiply $- 1$ by $- 1$ .

$x = - 1 \cdot b + 1 a$

Step 3.2.1.5.2

Multiply $a$ by $1$ .

$x = - 1 \cdot b + a$

Step 3.2.1.6

Rewrite $- 1 b$ as $- b$ .

$x = - b + a$

Step 3.2.1.7

Reorder $- b$ and $a$ .

$x = a - b$