Solve 7/x^2+x+1/x^2-x=6/x^2-1

$$\frac{ 7 }{ { x }^{ 2 } +x } + \frac{ 1 }{ { x }^{ 2 } -x } = \frac{ 6 }{ { x }^{ 2 } -1 }$$

Solve for x

$$x=3$$

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.

$$\left(x-1\right)\times 7+x+1=x\times 6$$

Use the distributive property to multiply x-1 by 7.

$$7x-7+x+1=x\times 6$$

Combine 7x and x to get 8x.

$$8x-7+1=x\times 6$$

Add -7 and 1 to get -6.

$$8x-6=x\times 6$$

Subtract x\times 6 from both sides.

$$8x-6-x\times 6=0$$

Combine 8x and -x\times 6 to get 2x.

$$2x-6=0$$

Add 6 to both sides. Anything plus zero gives itself.

$$2x=6$$

Divide both sides by 2.

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

Divide 6 by 2 to get 3.

$$x=3$$