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# Algebra Examples

Step 1

Write as an equation.

Step 2

Interchange the variables.

Step 3

Rewrite the equation as .

Multiply both sides by .

Simplify.

Simplify the left side.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Simplify the right side.

Move to the left of .

Solve for .

Add to both sides of the equation.

Divide each term in by and simplify.

Divide each term in by .

Simplify the left side.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Step 4

Replace with to show the final answer.

Step 5

To verify the inverse, check if and .

Evaluate .

Set up the composite result function.

Evaluate by substituting in the value of into .

Combine the numerators over the common denominator.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Combine the opposite terms in .

Add and .

Add and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Evaluate .

Set up the composite result function.

Evaluate by substituting in the value of into .

Simplify the numerator.

Apply the distributive property.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Subtract from .

Add and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Since and , then is the inverse of .