Solve 2x+1/x-2=2x+6/x

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

Solve for x

$$x=12$$

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.

$$x\left(2x+1\right)=\left(x-2\right)\left(2x+6\right)$$

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

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

Use the distributive property to multiply x-2 by 2x+6 and combine like terms.

$$2x^{2}+x=2x^{2}+2x-12$$

Subtract 2x^{2} from both sides.

$$2x^{2}+x-2x^{2}=2x-12$$

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

$$x=2x-12$$

Subtract 2x from both sides.

$$x-2x=-12$$

Combine x and -2x to get -x.

$$-x=-12$$

Multiply both sides by -1.

$$x=12$$