Solve x-1/x-2=2x^2+2/x^2-4+3-x/x+2

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

Solve for x

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

Steps for Solving Linear Equation

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

$$\left(x+2\right)\left(x-1\right)=2x^{2}+2+\left(x-2\right)\left(3-x\right)$$

Use the distributive property to multiply x+2 by x-1 and combine like terms.

$$x^{2}+x-2=2x^{2}+2+\left(x-2\right)\left(3-x\right)$$

Use the distributive property to multiply x-2 by 3-x and combine like terms.

$$x^{2}+x-2=2x^{2}+2+5x-x^{2}-6$$

Combine 2x^{2} and -x^{2} to get x^{2}.

$$x^{2}+x-2=x^{2}+2+5x-6$$

Subtract 6 from 2 to get -4.

$$x^{2}+x-2=x^{2}-4+5x$$

Subtract x^{2} from both sides.

$$x^{2}+x-2-x^{2}=-4+5x$$

Combine x^{2} and -x^{2} to get 0.

$$x-2=-4+5x$$

Subtract 5x from both sides.

$$x-2-5x=-4$$

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

$$-4x-2=-4$$

Add 2 to both sides.

$$-4x=-4+2$$

Add -4 and 2 to get -2.

$$-4x=-2$$

Divide both sides by -4.

$$x=\frac{-2}{-4}$$

Reduce the fraction \frac{-2}{-4} to lowest terms by extracting and canceling out -2.

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