Solve for x x/(x-3)=(2x)/2

Reduce the expression ${\displaystyle \frac{2x}{2}}$ by cancelling the common factors.

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

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

Remove parentheses.

The LCM of one and any expression is the expression.

Multiply each term in ${\displaystyle \frac{x}{x-3}=x}$ by ${\displaystyle x-3}$.

Simplify the left side.

Simplify the right side.

Since ${\displaystyle x}$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Factor ${\displaystyle x}$ out of ${\displaystyle x^2-4x}$.

If any individual factor on the left side of the equation is equal to ${\displaystyle 0}$, the entire expression will be equal to ${\displaystyle 0}$.

Set ${\displaystyle x}$ equal to ${\displaystyle 0}$.

Set ${\displaystyle x-4}$ equal to ${\displaystyle 0}$ and solve for ${\displaystyle x}$.

The final solution is all the values that make ${\displaystyle x(x-4)=0}$ true.