Basic Math Examples

$(a + b) k + g = y$

Step 1

Apply the distributive property.

$a k + b k + g = y$

Step 2

Subtract $g$ from both sides of the equation.

$a k + b k = y - g$

Step 3

Factor $k$ out of $a k + b k$ .

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Step 3.1

Factor $k$ out of $a k$ .

$k a + b k = y - g$

Step 3.2

Factor $k$ out of $b k$ .

$k a + k b = y - g$

Step 3.3

Factor $k$ out of $k a + k b$ .

$k (a + b) = y - g$

Step 4

Divide each term in $k (a + b) = y - g$ by $a + b$ and simplify.

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Step 4.1

Divide each term in $k (a + b) = y - g$ by $a + b$ .

$\frac{k (a + b)}{a + b} = \frac{y}{a + b} + \frac{- g}{a + b}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $a + b$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{k (a + b)}{a + b} = \frac{y}{a + b} + \frac{- g}{a + b}$

Step 4.2.1.2

Divide $k$ by $1$ .

$k = \frac{y}{a + b} + \frac{- g}{a + b}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$k = \frac{y}{a + b} - \frac{g}{a + b}$

Step 4.3.2

Combine the numerators over the common denominator.

$k = \frac{y - g}{a + b}$