Finite Math Examples

$\frac{x}{c - 3} = c x + 4$

Step 1

Multiply both sides by $c - 3$ .

$\frac{x}{c - 3} (c - 3) = (c x + 4) (c - 3)$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $c - 3$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{x}{c - 3} (c - 3) = (c x + 4) (c - 3)$

Step 2.1.1.2

Rewrite the expression.

$x = (c x + 4) (c - 3)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(c x + 4) (c - 3)$ .

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Step 2.2.1.1

Expand $(c x + 4) (c - 3)$ using the FOIL Method.

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Step 2.2.1.1.1

Apply the distributive property.

$x = c x (c - 3) + 4 (c - 3)$

Step 2.2.1.1.2

Apply the distributive property.

$x = c x c + c x \cdot - 3 + 4 (c - 3)$

Step 2.2.1.1.3

Apply the distributive property.

$x = c x c + c x \cdot - 3 + 4 c + 4 \cdot - 3$

Step 2.2.1.2

Simplify each term.

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Step 2.2.1.2.1

Multiply $c$ by $c$ by adding the exponents.

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Step 2.2.1.2.1.1

Move $c$ .

$x = c \cdot c x + c x \cdot - 3 + 4 c + 4 \cdot - 3$

Step 2.2.1.2.1.2

Multiply $c$ by $c$ .

$x = c^{2} x + c x \cdot - 3 + 4 c + 4 \cdot - 3$

Step 2.2.1.2.2

Move $- 3$ to the left of $c x$ .

$x = c^{2} x - 3 \cdot (c x) + 4 c + 4 \cdot - 3$

Step 2.2.1.2.3

Multiply $4$ by $- 3$ .

$x = c^{2} x - 3 c x + 4 c - 12$

Step 3

Solve for $x$ .

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Step 3.1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$c^{2} x - 3 c x + 4 c - 12 = x$

Step 3.2

Subtract $x$ from both sides of the equation.

$c^{2} x - 3 c x + 4 c - 12 - x = 0$

Step 3.3

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

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Step 3.3.1

Subtract $4 c$ from both sides of the equation.

$c^{2} x - 3 c x - 12 - x = - 4 c$

Step 3.3.2

Add $12$ to both sides of the equation.

$c^{2} x - 3 c x - x = - 4 c + 12$

Step 3.4

Factor $x$ out of $c^{2} x - 3 c x - x$ .

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Step 3.4.1

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

$x c^{2} - 3 c x - x = - 4 c + 12$

Step 3.4.2

Factor $x$ out of $- 3 c x$ .

$x c^{2} + x (- 3 c) - x = - 4 c + 12$

Step 3.4.3

Factor $x$ out of $- x$ .

$x c^{2} + x (- 3 c) + x \cdot - 1 = - 4 c + 12$

Step 3.4.4

Factor $x$ out of $x c^{2} + x (- 3 c)$ .

$x (c^{2} - 3 c) + x \cdot - 1 = - 4 c + 12$

Step 3.4.5

Factor $x$ out of $x (c^{2} - 3 c) + x \cdot - 1$ .

$x (c^{2} - 3 c - 1) = - 4 c + 12$

Step 3.5

Divide each term in $x (c^{2} - 3 c - 1) = - 4 c + 12$ by $c^{2} - 3 c - 1$ and simplify.

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Step 3.5.1

Divide each term in $x (c^{2} - 3 c - 1) = - 4 c + 12$ by $c^{2} - 3 c - 1$ .

$\frac{x (c^{2} - 3 c - 1)}{c^{2} - 3 c - 1} = \frac{- 4 c}{c^{2} - 3 c - 1} + \frac{12}{c^{2} - 3 c - 1}$

Step 3.5.2

Simplify the left side.

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Step 3.5.2.1

Cancel the common factor of $c^{2} - 3 c - 1$ .

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Step 3.5.2.1.1

Cancel the common factor.

$\frac{x (c^{2} - 3 c - 1)}{c^{2} - 3 c - 1} = \frac{- 4 c}{c^{2} - 3 c - 1} + \frac{12}{c^{2} - 3 c - 1}$

Step 3.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4 c}{c^{2} - 3 c - 1} + \frac{12}{c^{2} - 3 c - 1}$

Step 3.5.3

Simplify the right side.

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Step 3.5.3.1

Combine the numerators over the common denominator.

$x = \frac{- 4 c + 12}{c^{2} - 3 c - 1}$

Step 3.5.3.2

Factor $4$ out of $- 4 c + 12$ .

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Step 3.5.3.2.1

Factor $4$ out of $- 4 c$ .

$x = \frac{4 (- c) + 12}{c^{2} - 3 c - 1}$

Step 3.5.3.2.2

Factor $4$ out of $12$ .

$x = \frac{4 (- c) + 4 (3)}{c^{2} - 3 c - 1}$

Step 3.5.3.2.3

Factor $4$ out of $4 (- c) + 4 (3)$ .

$x = \frac{4 (- c + 3)}{c^{2} - 3 c - 1}$

Step 3.5.3.3

Factor $- 1$ out of $- c$ .

$x = \frac{4 (- (c) + 3)}{c^{2} - 3 c - 1}$

Step 3.5.3.4

Rewrite $3$ as $- 1 (- 3)$ .

$x = \frac{4 (- (c) - 1 (- 3))}{c^{2} - 3 c - 1}$

Step 3.5.3.5

Factor $- 1$ out of $- (c) - 1 (- 3)$ .

$x = \frac{4 (- (c - 3))}{c^{2} - 3 c - 1}$

Step 3.5.3.6

Simplify the expression.

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Step 3.5.3.6.1

Rewrite $- (c - 3)$ as $- 1 (c - 3)$ .

$x = \frac{4 (- 1 (c - 3))}{c^{2} - 3 c - 1}$

Step 3.5.3.6.2

Move the negative in front of the fraction.

$x = - \frac{4 (c - 3)}{c^{2} - 3 c - 1}$