Solve 6x/x^2-1+x/x-1=x+4/x-1

$$\frac { 6 x } { x ^ { 2 } - 1 } + \frac { x } { x - 1 } = \frac { x + 4 } { x - 1 }$$

Solve for x

$$x=2$$

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^{2}-1,x-1.

$$6x+\left(x+1\right)x=\left(x+1\right)\left(x+4\right)$$

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

$$6x+x^{2}+x=\left(x+1\right)\left(x+4\right)$$

Combine 6x and x to get 7x.

$$7x+x^{2}=\left(x+1\right)\left(x+4\right)$$

Use the distributive property to multiply x+1 by x+4 and combine like terms.

$$7x+x^{2}=x^{2}+5x+4$$

Subtract x^{2} from both sides.

$$7x+x^{2}-x^{2}=5x+4$$

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

$$7x=5x+4$$

Subtract 5x from both sides.

$$7x-5x=4$$

Combine 7x and -5x to get 2x.

$$2x=4$$

Divide both sides by 2.

$$x=\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$x=2$$