Solve x+1-4/x+1=x-1

$$x + 1 - \frac { 4 } { x + 1 } = x - 1$$

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 x+1.

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

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

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

Combine x and x to get 2x.

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

Subtract 4 from 1 to get -3.

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

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

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

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

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

Combine x and -x to get 0.

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

Subtract x^{2} from both sides.

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

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

$$2x-3=-1$$

Add 3 to both sides.

$$2x=-1+3$$

Add -1 and 3 to get 2.

$$2x=2$$

Divide both sides by 2.

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

Divide 2 by 2 to get 1.

$$x=1$$