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

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

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,0,3 since division by zero is not defined. Multiply both sides of the equation by 2x\left(x-3\right)\left(x+3\right), the least common multiple of x-3,2x,x+3.

$$2x\left(x+3\right)\times 2-\left(x^{2}-9\right)=2x\left(x-3\right)+x^{2}-9$$

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

$$\left(2x^{2}+6x\right)\times 2-\left(x^{2}-9\right)=2x\left(x-3\right)+x^{2}-9$$

Use the distributive property to multiply 2x^{2}+6x by 2.

$$4x^{2}+12x-\left(x^{2}-9\right)=2x\left(x-3\right)+x^{2}-9$$

To find the opposite of x^{2}-9, find the opposite of each term.

$$4x^{2}+12x-x^{2}+9=2x\left(x-3\right)+x^{2}-9$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}+12x+9=2x\left(x-3\right)+x^{2}-9$$

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

$$3x^{2}+12x+9=2x^{2}-6x+x^{2}-9$$

Combine 2x^{2} and x^{2} to get 3x^{2}.

$$3x^{2}+12x+9=3x^{2}-6x-9$$

Subtract 3x^{2} from both sides.

$$3x^{2}+12x+9-3x^{2}=-6x-9$$

Combine 3x^{2} and -3x^{2} to get 0.

$$12x+9=-6x-9$$

Add 6x to both sides.

$$12x+9+6x=-9$$

Combine 12x and 6x to get 18x.

$$18x+9=-9$$

Subtract 9 from both sides.

$$18x=-9-9$$

Subtract 9 from -9 to get -18.

$$18x=-18$$

Divide both sides by 18.

$$x=\frac{-18}{18}$$

Divide -18 by 18 to get -1.

$$x=-1$$