Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Combine the numerators over the common denominator.

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

Step 1.3

Simplify the numerator.

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Step 1.3.1

Apply the distributive property.

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

Step 1.3.2

Multiply $b$ by $b$ by adding the exponents.

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Step 1.3.2.1

Move $b$ .

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

Step 1.3.2.2

Multiply $b$ by $b$ .

$\frac{b x a + b^{2} x + a c}{a + b} = c$

Step 2

Multiply both sides by $a + b$ .

$\frac{b x a + b^{2} x + a c}{a + b} (a + b) = c (a + b)$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{b x a + b^{2} x + a c}{a + b} (a + b)$ .

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Step 3.1.1.1

Cancel the common factor of $a + b$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{b x a + b^{2} x + a c}{a + b} (a + b) = c (a + b)$

Step 3.1.1.1.2

Rewrite the expression.

$b x a + b^{2} x + a c = c (a + b)$

Step 3.1.1.2

Simplify the expression.

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Step 3.1.1.2.1

Move $x$ .

$b a x + b^{2} x + a c = c (a + b)$

Step 3.1.1.2.2

Reorder $b$ and $a$ .

$a b x + b^{2} x + a c = c (a + b)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $c (a + b)$ .

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Step 3.2.1.1

Apply the distributive property.

$a b x + b^{2} x + a c = c a + c b$

Step 3.2.1.2

Simplify with commuting.

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Step 3.2.1.2.1

Reorder $c$ and $a$ .

$a b x + b^{2} x + a c = a c + c b$

Step 3.2.1.2.2

Reorder $c$ and $b$ .

$a b x + b^{2} x + a c = a c + b c$

Step 4

Solve for $x$ .

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Step 4.1

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1.1

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

$a b x + b^{2} x = a c + b c - a c$

Step 4.1.2

Combine the opposite terms in $a c + b c - a c$ .

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Step 4.1.2.1

Subtract $a c$ from $a c$ .

$a b x + b^{2} x = b c + 0$

Step 4.1.2.2

Add $b c$ and $0$ .

$a b x + b^{2} x = b c$

Step 4.2

Factor $b x$ out of $a b x + b^{2} x$ .

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Step 4.2.1

Factor $b x$ out of $a b x$ .

$b x (a) + b^{2} x = b c$

Step 4.2.2

Factor $b x$ out of $b^{2} x$ .

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

Step 4.2.3

Factor $b x$ out of $b x (a) + b x (b)$ .

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

Step 4.3

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

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Step 4.3.1

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

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

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $b$ .

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Step 4.3.2.1.1

Cancel the common factor.

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

Step 4.3.2.1.2

Rewrite the expression.

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

Step 4.3.2.2

Cancel the common factor of $a + b$ .

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Step 4.3.2.2.1

Cancel the common factor.

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

Step 4.3.2.2.2

Divide $x$ by $1$ .

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

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Cancel the common factor of $b$ .

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Step 4.3.3.1.1

Cancel the common factor.

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

Step 4.3.3.1.2

Rewrite the expression.

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