Solve 6/(x+1)(x-1)+x/x-1=1

$$\frac { 6 } { ( x + 1 ) ( x - 1 ) } + \frac { x } { x - 1 } = 1$$

Solve for x

$$x=-7$$

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 \left(x+1\right)\left(x-1\right),x-1.

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

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

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

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$6+x^{2}+x=x^{2}-1$$

Subtract x^{2} from both sides.

$$6+x^{2}+x-x^{2}=-1$$

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

$$6+x=-1$$

Subtract 6 from both sides.

$$x=-1-6$$

Subtract 6 from -1 to get -7.

$$x=-7$$