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

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

Solve for x

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

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x, the least common multiple of x,2x.

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

Use the distributive property to multiply 2 by 2x+1.

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

Use the distributive property to multiply -2x by x+1.

$$4x+2-2x^{2}-2x=2x\times 2-\left(x-1\right)\times 2x$$

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

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

Multiply 2 and 2 to get 4.

$$2x+2-2x^{2}=4x-\left(x-1\right)\times 2x$$

Multiply -1 and 2 to get -2.

$$2x+2-2x^{2}=4x-2\left(x-1\right)x$$

Use the distributive property to multiply -2 by x-1.

$$2x+2-2x^{2}=4x+\left(-2x+2\right)x$$

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

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

Combine 4x and 2x to get 6x.

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

Subtract 6x from both sides.

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

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

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

Add 2x^{2} to both sides.

$$-4x+2-2x^{2}+2x^{2}=0$$

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

$$-4x+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$-4x=-2$$

Divide both sides by -4.

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

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

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