# Find the Inverse (3x-8)/(7-x) Interchange the variables.
Solve for .
Rewrite the equation as .
Solve for .
Multiply each term by and simplify.
Multiply each term in by .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify .
Apply the distributive property.
Reorder.
Move to the left of .
Rewrite using the commutative property of multiplication.
Add to both sides of the equation.
Add to both sides of the equation.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Combine the numerators over the common denominator.
Solve for and replace with .
Replace the with to show the final answer.
Set up the composite result function.
Evaluate by substituting in the value of into .
Remove parentheses.
Multiply the numerator and denominator of the complex fraction by .
Multiply by .
Combine.
Apply the distributive property.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify the numerator.
Factor out of .
Factor out of .
Factor out of .
Combine and .
To write as a fraction with a common denominator, multiply by .
Combine the numerators over the common denominator.
Rewrite in a factored form.
Apply the distributive property.
Multiply by .
Multiply by .
Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Simplify the denominator.
Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Reduce the expression by cancelling the common factors.
Factor out 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.
Rewrite the expression.
Since , is the inverse of .
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