Algebra Examples

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

Step 1

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

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

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.

$a + b, 1$

Step 2.2

Remove parentheses.

$a + b, 1$

Step 2.3

The LCM of one and any expression is the expression.

$a + b$

Step 3

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

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $a + b$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Rewrite the expression.

$a b = c (a + b)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$a b = c a + c b$

Step 4

Solve the equation.

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Step 4.1

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

$a b - c a = c b$

Step 4.2

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

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Step 4.2.1

Factor $a$ out of $a b$ .

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

Step 4.2.2

Factor $a$ out of $- c a$ .

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

Step 4.2.3

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

$a (b - c) = c b$

Step 4.3

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

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Step 4.3.1

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

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

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $b - c$ .

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Step 4.3.2.1.1

Cancel the common factor.

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

Step 4.3.2.1.2

Divide $a$ by $1$ .

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