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Precalculus Examples
Step 1
Write as an equation.
Step 2
Interchange the variables.
Step 3
Step 3.1
Rewrite the equation as .
Step 3.2
Subtract from both sides of the equation.
Step 3.3
Find the LCD of the terms in the equation.
Step 3.3.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 3.3.2
The LCM of one and any expression is the expression.
Step 3.4
Multiply each term in by to eliminate the fractions.
Step 3.4.1
Multiply each term in by .
Step 3.4.2
Simplify the left side.
Step 3.4.2.1
Cancel the common factor of .
Step 3.4.2.1.1
Move the leading negative in into the numerator.
Step 3.4.2.1.2
Cancel the common factor.
Step 3.4.2.1.3
Rewrite the expression.
Step 3.5
Solve the equation.
Step 3.5.1
Rewrite the equation as .
Step 3.5.2
Factor out of .
Step 3.5.2.1
Factor out of .
Step 3.5.2.2
Factor out of .
Step 3.5.2.3
Factor out of .
Step 3.5.3
Divide each term in by and simplify.
Step 3.5.3.1
Divide each term in by .
Step 3.5.3.2
Simplify the left side.
Step 3.5.3.2.1
Cancel the common factor of .
Step 3.5.3.2.1.1
Cancel the common factor.
Step 3.5.3.2.1.2
Divide by .
Step 3.5.3.3
Simplify the right side.
Step 3.5.3.3.1
Move the negative in front of the fraction.
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
Simplify the denominator.
Step 5.2.3.1
Subtract from .
Step 5.2.3.2
Add and .
Step 5.2.4
Cancel the common factor of and .
Step 5.2.4.1
Rewrite as .
Step 5.2.4.2
Move the negative in front of the fraction.
Step 5.2.5
Multiply the numerator by the reciprocal of the denominator.
Step 5.2.6
Multiply 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
Cancel the common factor of and .
Step 5.3.3.1.1
Rewrite as .
Step 5.3.3.1.2
Move the negative in front of the fraction.
Step 5.3.3.2
Multiply the numerator by the reciprocal of the denominator.
Step 5.3.3.3
Multiply by .
Step 5.3.3.4
Apply the distributive property.
Step 5.3.3.5
Multiply by .
Step 5.3.3.6
Apply the distributive property.
Step 5.3.3.7
Multiply .
Step 5.3.3.7.1
Multiply by .
Step 5.3.3.7.2
Multiply by .
Step 5.3.3.8
Multiply by .
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 .