Algebra Examples

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

Step 1

Multiply both sides by $b$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $b$ .

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Step 2.1.1.1

Cancel the common factor.

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

Step 2.1.1.2

Rewrite the expression.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

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

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Step 2.2.1.1

Apply the distributive property.

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

Step 2.2.1.2

Combine $\frac{x}{c}$ and $b$ .

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

Step 2.2.1.3

Simplify with commuting.

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Step 2.2.1.3.1

Reorder $x$ and $b$ .

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

Step 2.2.1.3.2

Reorder $\frac{b x}{c}$ and $a b$ .

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

Step 3

Solve for $x$ .

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Step 3.1

Subtract $\frac{b x}{c}$ from both sides of the equation.

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

Step 3.2

Find the LCD of the terms in the equation.

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Step 3.2.1

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

$1, c, 1$

Step 3.2.2

The LCM of one and any expression is the expression.

$c$

Step 3.3

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

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Step 3.3.1

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

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

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $c$ .

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Step 3.3.2.1.1

Move the leading negative in $- \frac{b x}{c}$ into the numerator.

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

Step 3.3.2.1.2

Cancel the common factor.

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

Step 3.3.2.1.3

Rewrite the expression.

$x c - b x = a b c$

Step 3.4

Solve the equation.

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Step 3.4.1

Factor $x$ out of $x c - b x$ .

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Step 3.4.1.1

Factor $x$ out of $x c$ .

$x (c) - b x = a b c$

Step 3.4.1.2

Factor $x$ out of $- b x$ .

$x (c) + x (- b) = a b c$

Step 3.4.1.3

Factor $x$ out of $x (c) + x (- b)$ .

$x (c - b) = a b c$

Step 3.4.2

Divide each term in $x (c - b) = a b c$ by $c - b$ and simplify.

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Step 3.4.2.1

Divide each term in $x (c - b) = a b c$ by $c - b$ .

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

Step 3.4.2.2

Simplify the left side.

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Step 3.4.2.2.1

Cancel the common factor of $c - b$ .

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Step 3.4.2.2.1.1

Cancel the common factor.

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

Step 3.4.2.2.1.2

Divide $x$ by $1$ .

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