Find the Inverse 12/x-18

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

The LCM of one and any expression is the expression.

Multiply each term in ${\displaystyle \frac{12}{y}=x+18}$ by ${\displaystyle y}$.

Simplify the left side.

Rewrite the equation as ${\displaystyle xy+18y=12}$.

Factor ${\displaystyle y}$ out of ${\displaystyle xy+18y}$.

Divide each term in ${\displaystyle y(x+18)=12}$ by ${\displaystyle x+18}$ and simplify.

Set up the composite result function.

Evaluate ${\displaystyle f^{-1}(\frac{12}{x}-18)}$ by substituting in the value of ${\displaystyle f}$ into ${\displaystyle f^{-1}}$.

Cancel the common factor of ${\displaystyle 12}$ and ${\displaystyle (\frac{12}{x}-18)+18}$.

Simplify the denominator.

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of ${\displaystyle 2}$.

Set up the composite result function.

Evaluate ${\displaystyle f\left(\frac{12}{x+18}\right)}$ by substituting in the value of ${\displaystyle f^{-1}}$ into ${\displaystyle f}$.

Simplify each term.

Combine the opposite terms in ${\displaystyle x+18-18}$.