Solve x+1/x-1+4/(1-x)^2=1

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

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

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

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

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.

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

Add -1 and 4 to get 3.

$$x^{2}+3=\left(x-1\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$x^{2}+3=x^{2}-2x+1$$

Subtract x^{2} from both sides.

$$x^{2}+3-x^{2}=-2x+1$$

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

$$3=-2x+1$$

Swap sides so that all variable terms are on the left hand side.

$$-2x+1=3$$

Subtract 1 from both sides.

$$-2x=3-1$$

Subtract 1 from 3 to get 2.

$$-2x=2$$

Divide both sides by -2.

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

Divide 2 by -2 to get -1.

$$x=-1$$