Solve 5/x+1+2x/x^2-1=1/x+1

$$\frac { 5 } { x + 1 } + \frac { 2 x } { x ^ { 2 } - 1 } = \frac { 1 } { x + 1 }$$

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

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

$$\left(x-1\right)\times 5+2x=x-1$$

Use the distributive property to multiply x-1 by 5.

$$5x-5+2x=x-1$$

Combine 5x and 2x to get 7x.

$$7x-5=x-1$$

Subtract x from both sides.

$$7x-5-x=-1$$

Combine 7x and -x to get 6x.

$$6x-5=-1$$

Add 5 to both sides.

$$6x=-1+5$$

Add -1 and 5 to get 4.

$$6x=4$$

Divide both sides by 6.

$$x=\frac{4}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$x=\frac{2}{3}$$