Solve 3/2x-4-2/3x-6=x/x^2-4x+4

$$\frac{ 3 }{ 2x-4 } - \frac{ 2 }{ 3x-6 } = \frac{ x }{ { x }^{ 2 } -4x+4 }$$

Solve for x

$$x=-10$$

Steps for Solving Linear Equation

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by 6\left(x-2\right)^{2}, the least common multiple of 2x-4,3x-6,x^{2}-4x+4.

$$\left(3x-6\right)\times 3-\left(2x-4\right)\times 2=6x$$

Use the distributive property to multiply 3x-6 by 3.

$$9x-18-\left(2x-4\right)\times 2=6x$$

Use the distributive property to multiply 2x-4 by 2.

$$9x-18-\left(4x-8\right)=6x$$

To find the opposite of 4x-8, find the opposite of each term.

$$9x-18-4x+8=6x$$

Combine 9x and -4x to get 5x.

$$5x-18+8=6x$$

Add -18 and 8 to get -10.

$$5x-10=6x$$

Subtract 6x from both sides.

$$5x-10-6x=0$$

Combine 5x and -6x to get -x.

$$-x-10=0$$

Add 10 to both sides. Anything plus zero gives itself.

$$-x=10$$

Multiply both sides by -1.

$$x=-10$$