Solve 7/x^2+x+3/x^2-x=1/x^2-1

$$\frac{ 7 }{ { x }^{ 2 } +x } + \frac{ 3 }{ { x }^{ 2 } -x } = \frac{ 1 }{ { x }^{ 2 } -1 }$$

Solve for x

$$x=\frac{4}{9}\approx 0.444444444$$

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.

$$\left(x-1\right)\times 7+\left(x+1\right)\times 3=x$$

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

$$7x-7+\left(x+1\right)\times 3=x$$

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

$$7x-7+3x+3=x$$

Combine 7x and 3x to get 10x.

$$10x-7+3=x$$

Add -7 and 3 to get -4.

$$10x-4=x$$

Subtract x from both sides.

$$10x-4-x=0$$

Combine 10x and -x to get 9x.

$$9x-4=0$$

Add 4 to both sides. Anything plus zero gives itself.

$$9x=4$$

Divide both sides by 9.

$$x=\frac{4}{9}$$