Find the Inverse 7/x+5

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 ${\displaystyle \frac{7}{y}=x-5}$ by ${\displaystyle y}$.

Simplify the left side.

Rewrite the equation as ${\displaystyle xy-5y=7}$.

Factor ${\displaystyle y}$ out of ${\displaystyle xy-5y}$.

Divide each term in ${\displaystyle y(x-5)=7}$ by ${\displaystyle x-5}$ and simplify.

Set up the composite result function.

Evaluate ${\displaystyle f^{-1}(\frac{7}{x}+5)}$ by substituting in the value of ${\displaystyle f}$ into ${\displaystyle f^{-1}}$.

Simplify the denominator.

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of ${\displaystyle 7}$.

Set up the composite result function.

Evaluate ${\displaystyle f\left(\frac{7}{x-5}\right)}$ by substituting in the value of ${\displaystyle f^{-1}}$ into ${\displaystyle f}$.

Simplify each term.

Combine the opposite terms in ${\displaystyle x-5+5}$.