Solve 2/3x+1/2=1/x+1

$$\frac { 2 } { 3 x } + \frac { 1 } { 2 } = \frac { 1 } { x } + 1$$

Solve for x

$$x=-\frac{2}{3}\approx -0.666666667$$

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 6x, the least common multiple of 3x,2,x.

$$2\times 2+6x\times \frac{1}{2}=6+6x$$

Multiply 2 and 2 to get 4.

$$4+6x\times \frac{1}{2}=6+6x$$

Multiply 6 and \frac{1}{2} to get 3.

$$4+3x=6+6x$$

Subtract 6x from both sides.

$$4+3x-6x=6$$

Combine 3x and -6x to get -3x.

$$4-3x=6$$

Subtract 4 from both sides.

$$-3x=6-4$$

Subtract 4 from 6 to get 2.

$$-3x=2$$

Divide both sides by -3.

$$x=\frac{2}{-3}$$

Fraction \frac{2}{-3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$x=-\frac{2}{3}$$