Solve for x 1/(3x-3)+1/(4x+4)=1/(12x-12)

Factor ${\displaystyle 3}$ out of ${\displaystyle 3x-3}$.

Factor ${\displaystyle 4}$ out of ${\displaystyle 4x+4}$.

Factor ${\displaystyle 12}$ out of ${\displaystyle 12x-12}$.

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

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

Since ${\displaystyle 3}$ has no factors besides ${\displaystyle 1}$ and ${\displaystyle 3}$.

${\displaystyle 4}$ has factors of ${\displaystyle 2}$ and ${\displaystyle 2}$.

The prime factors for ${\displaystyle 12}$ are ${\displaystyle 2\cdot 2\cdot 3}$.

Multiply ${\displaystyle 2\cdot 2\cdot 3}$.

The factor for ${\displaystyle x-1}$ is ${\displaystyle x-1}$ itself.

The factor for ${\displaystyle x+1}$ is ${\displaystyle x+1}$ itself.

The factor for ${\displaystyle x-1}$ is ${\displaystyle x-1}$ itself.

The LCM of ${\displaystyle x-1,x+1,x-1}$ is the result of multiplying all factors the greatest number of times they occur in either term.

The Least Common Multiple ${\displaystyle \mathrm{LCM}}$ of some numbers is the smallest number that the numbers are factors of.

Multiply each term in ${\displaystyle \frac{1}{3(x-1)}+\frac{1}{4(x+1)}=\frac{1}{12(x-1)}}$ by ${\displaystyle 12(x-1)(x+1)}$.

Simplify the left side.

Simplify the right side.

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

Move all terms not containing ${\displaystyle x}$ to the right side of the equation.

Divide each term in ${\displaystyle 6x=0}$ by ${\displaystyle 6}$ and simplify.