Solve x+2/3x+x-2/2x=3

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

Solve for x

$$x=-\frac{2}{13}\approx -0.153846154$$

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,2x.

$$2\left(x+2\right)+3\left(x-2\right)=18x$$

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

$$2x+4+3\left(x-2\right)=18x$$

Use the distributive property to multiply 3 by x-2.

$$2x+4+3x-6=18x$$

Combine 2x and 3x to get 5x.

$$5x+4-6=18x$$

Subtract 6 from 4 to get -2.

$$5x-2=18x$$

Subtract 18x from both sides.

$$5x-2-18x=0$$

Combine 5x and -18x to get -13x.

$$-13x-2=0$$

Add 2 to both sides. Anything plus zero gives itself.

$$-13x=2$$

Divide both sides by -13.

$$x=\frac{2}{-13}$$

Fraction \frac{2}{-13} can be rewritten as -\frac{2}{13} by extracting the negative sign.

$$x=-\frac{2}{13}$$