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

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

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -1,0 since division by zero is not defined. Multiply both sides of the equation by \left(x+1\right)x^{2}, the least common multiple of x,x+1,x^{2}.

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

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

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

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

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

Use the distributive property to multiply x+1 by 3.

$$2x^{2}+2x-x^{2}\times 2=3x+3$$

Subtract 3x from both sides.

$$2x^{2}+2x-x^{2}\times 2-3x=3$$

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

$$2x^{2}-x-x^{2}\times 2=3$$

Multiply -1 and 2 to get -2.

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

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

$$-x=3$$

Multiply both sides by -1.

$$x=-3$$