Algebra Examples

$\frac{c}{a - b} = 1$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$a - b, 1$

Step 1.2

Remove parentheses.

$a - b, 1$

Step 1.3

The LCM of one and any expression is the expression.

$a - b$

Step 2

Multiply each term in $\frac{c}{a - b} = 1$ by $a - b$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{c}{a - b} = 1$ by $a - b$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $a - b$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Rewrite the expression.

$c = 1 (a - b)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $a - b$ by $1$ .

$c = a - b$

Step 3

Solve the equation.

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Step 3.1

Rewrite the equation as $a - b = c$ .

$a - b = c$

Step 3.2

Subtract $a$ from both sides of the equation.

$- b = c - a$

Step 3.3

Divide each term in $- b = c - a$ by $- 1$ and simplify.

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Step 3.3.1

Divide each term in $- b = c - a$ by $- 1$ .

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

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Dividing two negative values results in a positive value.

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

Step 3.3.2.2

Divide $b$ by $1$ .

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

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Simplify each term.

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Step 3.3.3.1.1

Move the negative one from the denominator of $\frac{c}{- 1}$ .

$b = - 1 \cdot c + \frac{- a}{- 1}$

Step 3.3.3.1.2

Rewrite $- 1 \cdot c$ as $- c$ .

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

Step 3.3.3.1.3

Dividing two negative values results in a positive value.

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

Step 3.3.3.1.4

Divide $a$ by $1$ .

$b = - c + a$