# Algebra Examples

Step 1

Write as an equation.

Step 2

Interchange the variables.

Step 3

Step 3.1

Rewrite the equation as .

Step 3.2

Add to both sides of the equation.

Step 3.3

Divide each term in by and simplify.

Step 3.3.1

Divide each term in by .

Step 3.3.2

Simplify the left side.

Step 3.3.2.1

Cancel the common factor of .

Step 3.3.2.1.1

Cancel the common factor.

Step 3.3.2.1.2

Divide by .

Step 4

Replace with to show the final answer.

Step 5

Step 5.1

To verify the inverse, check if and .

Step 5.2

Evaluate .

Step 5.2.1

Set up the composite result function.

Step 5.2.2

Evaluate by substituting in the value of into .

Step 5.2.3

Combine the numerators over the common denominator.

Step 5.2.4

Combine the opposite terms in .

Step 5.2.4.1

Add and .

Step 5.2.4.2

Add and .

Step 5.2.5

Cancel the common factor of .

Step 5.2.5.1

Cancel the common factor.

Step 5.2.5.2

Divide by .

Step 5.3

Evaluate .

Step 5.3.1

Set up the composite result function.

Step 5.3.2

Evaluate by substituting in the value of into .

Step 5.3.3

Simplify each term.

Step 5.3.3.1

Apply the distributive property.

Step 5.3.3.2

Cancel the common factor of .

Step 5.3.3.2.1

Cancel the common factor.

Step 5.3.3.2.2

Rewrite the expression.

Step 5.3.3.3

Cancel the common factor of .

Step 5.3.3.3.1

Cancel the common factor.

Step 5.3.3.3.2

Rewrite the expression.

Step 5.3.4

Combine the opposite terms in .

Step 5.3.4.1

Subtract from .

Step 5.3.4.2

Add and .

Step 5.4

Since and , then is the inverse of .