# Algebra Examples

Step 1

Write as an equation.

Step 2

Interchange the variables.

Step 3

Rewrite the equation as .

Subtract from 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 .

Simplify the right side.

Move the negative in front of the fraction.

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

Simplify .

Combine the numerators over the common denominator.

Rewrite as .

Multiply by .

Combine and simplify the denominator.

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Use to rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Evaluate the exponent.

Simplify the numerator.

Rewrite as .

Raise to the power of .

Simplify with factoring out.

Combine using the product rule for radicals.

Reorder factors in .

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 .

Simplify the numerator.

Subtract from .

Add and .

Multiply by .

Rewrite as .

Pull terms out from under the radical, assuming real numbers.

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 each term.

Apply the product rule to .

Simplify the numerator.

Rewrite as .

Use to rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Simplify.

Apply the distributive property.

Multiply by .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Raise to the power of .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Combine the opposite terms in .

Add and .

Add and .

Since and , then is the inverse of .