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

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

Solve for m

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

$$x\neq 3\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x\left(x-3\right), the least common multiple of x-3,x.

$$x\left(2m+x\right)+x\left(x-3\right)\left(-1\right)=\left(x-3\right)\times 2$$

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

$$2xm+x^{2}+x\left(x-3\right)\left(-1\right)=\left(x-3\right)\times 2$$

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

$$2xm+x^{2}+\left(x^{2}-3x\right)\left(-1\right)=\left(x-3\right)\times 2$$

Use the distributive property to multiply x^{2}-3x by -1.

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

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

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

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

$$2xm+3x=2x-6$$

Subtract 3x from both sides.

$$2xm=2x-6-3x$$

Combine 2x and -3x to get -x.

$$2xm=-x-6$$

Divide both sides by 2x.

$$\frac{2xm}{2x}=\frac{-x-6}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$m=\frac{-x-6}{2x}$$

Divide -x-6 by 2x.

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

Solve for x

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

$$m\neq -\frac{3}{2}\text{ and }m\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

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

$$x\left(2m+x\right)+x\left(x-3\right)\left(-1\right)=\left(x-3\right)\times 2$$

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

$$2xm+x^{2}+x\left(x-3\right)\left(-1\right)=\left(x-3\right)\times 2$$

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

$$2xm+x^{2}+\left(x^{2}-3x\right)\left(-1\right)=\left(x-3\right)\times 2$$

Use the distributive property to multiply x^{2}-3x by -1.

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

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

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

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

$$2xm+3x=2x-6$$

Subtract 2x from both sides.

$$2xm+3x-2x=-6$$

Combine 3x and -2x to get x.

$$2xm+x=-6$$

Combine all terms containing x.

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

Divide both sides by 2m+1.

$$\frac{\left(2m+1\right)x}{2m+1}=-\frac{6}{2m+1}$$

Dividing by 2m+1 undoes the multiplication by 2m+1.

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

Variable x cannot be equal to any of the values 3,0.

$$x=-\frac{6}{2m+1}\text{, }x\neq 3\text{ and }x\neq 0$$