Algebra Examples

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

Step 1

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

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

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $b$ .

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Step 2.1.1

Cancel the common factor.

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

Step 2.1.2

Divide $x$ by $1$ .

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

Step 3

Simplify the right side.

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Step 3.1

Combine the numerators over the common denominator.

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

Step 3.2

To write $c$ as a fraction with a common denominator, multiply by $\frac{a + b}{a + b}$ .

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

Step 3.3

Combine the numerators over the common denominator.

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

Step 3.4

Simplify the numerator.

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Step 3.4.1

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

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Step 3.4.1.1

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

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

Step 3.4.1.2

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

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

Step 3.4.2

Subtract $a$ from $a$ .

$x = \frac{\frac{c (b + 0)}{a + b}}{b}$

Step 3.4.3

Add $b$ and $0$ .

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

Step 3.5

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.6

Cancel the common factor of $b$ .

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Step 3.6.1

Factor $b$ out of $c b$ .

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

Step 3.6.2

Cancel the common factor.

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

Step 3.6.3

Rewrite the expression.

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