Algebra Examples

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

Step 1

Add $b$ to both sides of the equation.

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

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$x, 1, 1$

Step 2.2

The LCM of one and any expression is the expression.

$x$

Step 3

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

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $x$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Rewrite the expression.

$a = c x + b x$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $c x + b x = a$ .

$c x + b x = a$

Step 4.2

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

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Step 4.2.1

Factor $x$ out of $c x$ .

$x c + b x = a$

Step 4.2.2

Factor $x$ out of $b x$ .

$x c + x b = a$

Step 4.2.3

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

$x (c + b) = a$

Step 4.3

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

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Step 4.3.1

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

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

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $c + b$ .

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Step 4.3.2.1.1

Cancel the common factor.

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

Step 4.3.2.1.2

Divide $x$ by $1$ .

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