Finite Math Examples

$c A - 1 = \frac{1}{c} \cdot A - 1$

Step 1

Combine $\frac{1}{c}$ and $A$ .

$c A - 1 = \frac{A}{c} - 1$

Step 2

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

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Step 2.1

Add $1$ to both sides of the equation.

$c A = \frac{A}{c} - 1 + 1$

Step 2.2

Combine the opposite terms in $\frac{A}{c} - 1 + 1$ .

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Step 2.2.1

Add $- 1$ and $1$ .

$c A = \frac{A}{c} + 0$

Step 2.2.2

Add $\frac{A}{c}$ and $0$ .

$c A = \frac{A}{c}$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1, c$

Step 3.2

The LCM of one and any expression is the expression.

$c$

Step 4

Multiply each term in $c A = \frac{A}{c}$ by $c$ to eliminate the fractions.

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Step 4.1

Multiply each term in $c A = \frac{A}{c}$ by $c$ .

$c A c = \frac{A}{c} c$

Step 4.2

Simplify the left side.

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Step 4.2.1

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

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Step 4.2.1.1

Move $c$ .

$c \cdot c A = \frac{A}{c} c$

Step 4.2.1.2

Multiply $c$ by $c$ .

$c^{2} A = \frac{A}{c} c$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $c$ .

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Step 4.3.1.1

Cancel the common factor.

$c^{2} A = \frac{A}{c} c$

Step 4.3.1.2

Rewrite the expression.

$c^{2} A = A$

Step 5

Solve the equation.

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Step 5.1

Divide each term in $c^{2} A = A$ by $A$ and simplify.

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Step 5.1.1

Divide each term in $c^{2} A = A$ by $A$ .

$\frac{c^{2} A}{A} = \frac{A}{A}$

Step 5.1.2

Simplify the left side.

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Step 5.1.2.1

Cancel the common factor of $A$ .

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Step 5.1.2.1.1

Cancel the common factor.

$\frac{c^{2} A}{A} = \frac{A}{A}$

Step 5.1.2.1.2

Divide $c^{2}$ by $1$ .

$c^{2} = \frac{A}{A}$

Step 5.1.3

Simplify the right side.

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Step 5.1.3.1

Cancel the common factor of $A$ .

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Step 5.1.3.1.1

Cancel the common factor.

$c^{2} = \frac{A}{A}$

Step 5.1.3.1.2

Rewrite the expression.

$c^{2} = 1$

Step 5.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$c = \pm \sqrt{1}$

Step 5.3

Any root of $1$ is $1$ .

$c = \pm 1$

Step 5.4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.4.1

First, use the positive value of the $\pm$ to find the first solution.

$c = 1$

Step 5.4.2

Next, use the negative value of the $\pm$ to find the second solution.

$c = - 1$

Step 5.4.3

The complete solution is the result of both the positive and negative portions of the solution.

$c = 1, - 1$