Finite Math Examples

$a b + c = b c - a$

Step 1

Add $a$ to both sides of the equation.

$a b + c + a = b c$

Step 2

Subtract $c$ from both sides of the equation.

$a b + a = b c - c$

Step 3

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

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Step 3.1

Factor $a$ out of $a b$ .

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

Step 3.2

Raise $a$ to the power of $1$ .

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

Step 3.3

Factor $a$ out of $a^{1}$ .

$a (b) + a \cdot 1 = b c - c$

Step 3.4

Factor $a$ out of $a (b) + a \cdot 1$ .

$a (b + 1) = b c - c$

Step 4

Divide each term in $a (b + 1) = b c - c$ by $b + 1$ and simplify.

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Step 4.1

Divide each term in $a (b + 1) = b c - c$ by $b + 1$ .

$\frac{a (b + 1)}{b + 1} = \frac{b c}{b + 1} + \frac{- c}{b + 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $b + 1$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{a (b + 1)}{b + 1} = \frac{b c}{b + 1} + \frac{- c}{b + 1}$

Step 4.2.1.2

Divide $a$ by $1$ .

$a = \frac{b c}{b + 1} + \frac{- c}{b + 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Combine the numerators over the common denominator.

$a = \frac{b c - c}{b + 1}$

Step 4.3.2

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

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Step 4.3.2.1

Factor $c$ out of $b c$ .

$a = \frac{c b - c}{b + 1}$

Step 4.3.2.2

Factor $c$ out of $- c$ .

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

Step 4.3.2.3

Factor $c$ out of $c b + c \cdot - 1$ .

$a = \frac{c (b - 1)}{b + 1}$