Solve 1/x-1-2/x-2=1/2x-2-7/3(2x-4)

$$\frac { 1 } { x - 1 } - \frac { 2 } { x - 2 } = \frac { 1 } { 2 x - 2 } - \frac { 7 } { 3 ( 2 x - 4 ) }$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

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 6\left(x-2\right)\left(x-1\right), the least common multiple of x-1,x-2,2x-2,3\left(2x-4\right).

$$6x-12-\left(6x-6\right)\times 2=3x-6-\left(x-1\right)\times 7$$

Use the distributive property to multiply 6x-6 by 2.

$$6x-12-\left(12x-12\right)=3x-6-\left(x-1\right)\times 7$$

To find the opposite of 12x-12, find the opposite of each term.

$$6x-12-12x+12=3x-6-\left(x-1\right)\times 7$$

Combine 6x and -12x to get -6x.

$$-6x-12+12=3x-6-\left(x-1\right)\times 7$$

Add -12 and 12 to get 0.

$$-6x=3x-6-\left(x-1\right)\times 7$$

Use the distributive property to multiply x-1 by 7.

$$-6x=3x-6-\left(7x-7\right)$$

To find the opposite of 7x-7, find the opposite of each term.

$$-6x=3x-6-7x+7$$

Combine 3x and -7x to get -4x.

$$-6x=-4x-6+7$$

Add -6 and 7 to get 1.

$$-6x=-4x+1$$

Add 4x to both sides.

$$-6x+4x=1$$

Combine -6x and 4x to get -2x.

$$-2x=1$$

Divide both sides by -2.

$$x=\frac{1}{-2}$$

Fraction \frac{1}{-2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$x=-\frac{1}{2}$$