Solve x+1/x=x-2/x-1

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

Solve for x

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

Steps for Solving Linear Equation

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 x\left(x-1\right), the least common multiple of x,x-1.

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

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

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

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

$$x^{2}-1=x^{2}-2x$$

Subtract x^{2} from both sides.

$$x^{2}-1-x^{2}=-2x$$

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

$$-1=-2x$$

Swap sides so that all variable terms are on the left hand side.

$$-2x=-1$$

Divide both sides by -2.

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

Fraction \frac{-1}{-2} can be simplified to \frac{1}{2} by removing the negative sign from both the numerator and the denominator.

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