Solve 2-2x/x(x-1)=4(x-1)/x(2-2x)

$$\frac { 2 - 2 x } { x ( x - 1 ) } = \frac { 4 ( x - 1 ) } { x ( 2 - 2 x ) }$$

Solve for x (complex solution)

$$x\in \mathrm{C}\setminus 0,1$$

Solution Steps

Variable x cannot be equal to any of the values 0,1 since division by zero is not defined. Multiply both sides of the equation by 2x\left(x-1\right), the least common multiple of x\left(x-1\right),x\left(2-2x\right).

$$2\left(2-2x\right)=-4\left(x-1\right)$$

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

$$4-4x=-4\left(x-1\right)$$

Use the distributive property to multiply -4 by x-1.

$$4-4x=-4x+4$$

Add 4x to both sides.

$$4-4x+4x=4$$

Combine -4x and 4x to get 0.

$$4=4$$

Compare 4 and 4.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Variable x cannot be equal to any of the values 1,0.

$$x\in \mathrm{C}\setminus 0,1$$

Solve for x

$$x\in \mathrm{R}\setminus 0,1$$

Solution Steps

Variable x cannot be equal to any of the values 0,1 since division by zero is not defined. Multiply both sides of the equation by 2x\left(x-1\right), the least common multiple of x\left(x-1\right),x\left(2-2x\right).

$$2\left(2-2x\right)=-4\left(x-1\right)$$

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

$$4-4x=-4\left(x-1\right)$$

Use the distributive property to multiply -4 by x-1.

$$4-4x=-4x+4$$

Add 4x to both sides.

$$4-4x+4x=4$$

Combine -4x and 4x to get 0.

$$4=4$$

Compare 4 and 4.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$

Variable x cannot be equal to any of the values 1,0.

$$x\in \mathrm{R}\setminus 0,1$$