Find the Inverse 2/x-6

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 ${\displaystyle \frac{2}{y}=x+6}$ by ${\displaystyle y}$.

Simplify the left side.

Rewrite the equation as ${\displaystyle xy+6y=2}$.

Factor ${\displaystyle y}$ out of ${\displaystyle xy+6y}$.

Divide each term in ${\displaystyle y(x+6)=2}$ by ${\displaystyle x+6}$ and simplify.

Set up the composite result function.

Evaluate ${\displaystyle f^{-1}(\frac{2}{x}-6)}$ by substituting in the value of ${\displaystyle f}$ into ${\displaystyle f^{-1}}$.

Cancel the common factor of ${\displaystyle 2}$ and ${\displaystyle (\frac{2}{x}-6)+6}$.

Simplify the denominator.

Multiply the numerator by the reciprocal of the denominator.

Multiply ${\displaystyle x}$ by ${\displaystyle 1}$.

Set up the composite result function.

Evaluate ${\displaystyle f\left(\frac{2}{x+6}\right)}$ by substituting in the value of ${\displaystyle f^{-1}}$ into ${\displaystyle f}$.

Simplify each term.

Combine the opposite terms in ${\displaystyle x+6-6}$.