Algebra Examples

Step 1
Write as an equation.
Step 2
Interchange the variables.
Step 3
Solve for .
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Rewrite the equation as .
Subtract from both sides of the equation.
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify the right side.
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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 .
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Combine the numerators over the common denominator.
Rewrite as .
Multiply by .
Combine and simplify the denominator.
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Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
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Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Simplify the numerator.
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Rewrite as .
Raise to the power of .
Simplify with factoring out.
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Combine using the product rule for radicals.
Reorder factors in .
Step 4
Replace with to show the final answer.
Step 5
Verify if is the inverse of .
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To verify the inverse, check if and .
Evaluate .
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Set up the composite result function.
Evaluate by substituting in the value of into .
Simplify the numerator.
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Subtract from .
Add and .
Multiply by .
Rewrite as .
Pull terms out from under the radical, assuming real numbers.
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Evaluate .
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Set up the composite result function.
Evaluate by substituting in the value of into .
Simplify each term.
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Apply the product rule to .
Simplify the numerator.
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Rewrite as .
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Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Simplify.
Apply the distributive property.
Multiply by .
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Raise to the power of .
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Combine the opposite terms in .
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Add and .
Add and .
Since and , then is the inverse of .
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