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

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

Solve for x

$$x=\frac{1}{4}=0.25$$

Steps for Solving Linear Equation

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

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

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

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

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

$$3x-3+2x+2=x$$

Combine 3x and 2x to get 5x.

$$5x-3+2=x$$

Add -3 and 2 to get -1.

$$5x-1=x$$

Subtract x from both sides.

$$5x-1-x=0$$

Combine 5x and -x to get 4x.

$$4x-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$4x=1$$

Divide both sides by 4.

$$x=\frac{1}{4}$$