Solve 1/x-1-2/x-2-3/2x-2+frac{7/3}{2x-4}=0

$$\frac{ 1 }{ x-1 } - \frac{ 2 }{ x-2 } - \frac{ 3 }{ 2x-2 } + \frac{ \frac{ 7 }{ 3 } }{ 2x-4 } =0$$

Solve for x

$$x = \frac{11}{8} = 1\frac{3}{8} = 1.375$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 1,2 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-2\right)\left(x-1\right), the least common multiple of x-1,x-2,2x-2,2x-4.

$$2x-4-\left(2x-2\right)\times 2-\left(x-2\right)\times 3+\left(x-1\right)\times \frac{7}{3}=0$$

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

$$2x-4-\left(4x-4\right)-\left(x-2\right)\times 3+\left(x-1\right)\times \frac{7}{3}=0$$

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

$$2x-4-4x+4-\left(x-2\right)\times 3+\left(x-1\right)\times \frac{7}{3}=0$$

Combine 2x and -4x to get -2x.

$$-2x-4+4-\left(x-2\right)\times 3+\left(x-1\right)\times \frac{7}{3}=0$$

Add -4 and 4 to get 0.

$$-2x-\left(x-2\right)\times 3+\left(x-1\right)\times \frac{7}{3}=0$$

Use the distributive property to multiply x-1 by \frac{7}{3}.

$$-2x-\left(x-2\right)\times 3+\frac{7}{3}x-\frac{7}{3}=0$$

Combine -2x and \frac{7}{3}x to get \frac{1}{3}x.

$$\frac{1}{3}x-\left(x-2\right)\times 3-\frac{7}{3}=0$$

Use the distributive property to multiply x-2 by 3.

$$\frac{1}{3}x-\left(3x-6\right)-\frac{7}{3}=0$$

To find the opposite of 3x-6, find the opposite of each term.

$$\frac{1}{3}x-3x+6-\frac{7}{3}=0$$

Combine \frac{1}{3}x and -3x to get -\frac{8}{3}x.

$$-\frac{8}{3}x+6-\frac{7}{3}=0$$

Subtract \frac{7}{3} from 6 to get \frac{11}{3}.

$$-\frac{8}{3}x+\frac{11}{3}=0$$

Subtract \frac{11}{3} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{8}{3}x=-\frac{11}{3}$$

Multiply both sides by -\frac{3}{8}, the reciprocal of -\frac{8}{3}.

$$x=-\frac{11}{3}\left(-\frac{3}{8}\right)$$

Multiply -\frac{11}{3} and -\frac{3}{8} to get \frac{11}{8}.

$$x=\frac{11}{8}$$