# Algebra Examples

Step 1
Write as an equation.
Step 2
Interchange the variables.
Step 3
Solve for .
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
Verify if is the inverse of .
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
Step 5.2.4.2
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