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

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

Solve for x

$$x=-5$$

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}-1,1-x.

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

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

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

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

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

To find the opposite of -x-x^{2}, find the opposite of each term.

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

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.

$$4+x+x^{2}=x^{2}-1$$

Subtract x^{2} from both sides.

$$4+x+x^{2}-x^{2}=-1$$

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

$$4+x=-1$$

Subtract 4 from both sides.

$$x=-1-4$$

Subtract 4 from -1 to get -5.

$$x=-5$$