Solve the Rational Equation for x ((x+4)(x-2))/(9(x-2))=(x+4)/9

Cancel the common factor.

Rewrite the expression.

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

Since ${\displaystyle 9,9}$ contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part ${\displaystyle 9,9}$ then find LCM for the variable part .

The LCM is the smallest positive number that all of the numbers divide into evenly.

${\displaystyle 9}$ has factors of ${\displaystyle 3}$ and ${\displaystyle 3}$.

Multiply ${\displaystyle 3}$ by ${\displaystyle 3}$.

Multiply each term in ${\displaystyle \frac{x+4}{9}=\frac{x+4}{9}}$ by ${\displaystyle 9}$.

Simplify the left side.

Simplify the right side.

Move all terms containing ${\displaystyle x}$ to the left side of the equation.

Since ${\displaystyle 4=4}$, the equation will always be true.