Solve 1/e^2-1/x+1=0

$$\frac { 1 } { e ^ { 2 } } - \frac { 1 } { x + 1 } = 0$$

Solve for x

$$x=e^{2}-1\approx 6.389056099$$

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.

$$\left(x+1\right)e^{-2}-1=0$$

Use the distributive property to multiply x+1 by e^{-2}.

$$xe^{-2}+e^{-2}-1=0$$

Subtract e^{-2} from both sides. Anything subtracted from zero gives its negation.

$$xe^{-2}-1=-e^{-2}$$

Add 1 to both sides.

$$xe^{-2}=-e^{-2}+1$$

The equation is in standard form.

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

Divide both sides by e^{-2}.

$$\frac{\frac{1}{e^{2}}xe^{2}}{1}=\frac{\left(-\frac{1}{e^{2}}+1\right)e^{2}}{1}$$

Dividing by e^{-2} undoes the multiplication by e^{-2}.

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

Divide -\frac{1}{e^{2}}+1 by e^{-2}.

$$x=e^{2}-1$$

Variable x cannot be equal to -1.

$$x=e^{2}-1\text{, }x\neq -1$$