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

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

Solve for x

$$x=6$$

Steps for Solving Linear Equation

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

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

Multiply x and x to get x^{2}.

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

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

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

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

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

Combine 3x and -2x to get x.

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

Subtract x from both sides.

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

Subtract x^{2} from both sides.

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

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

$$-x=-6$$

Multiply both sides by -1.

$$x=6$$