Solve 1/x_{1}+1/x_{2}=-1

$$\frac { 1 } { x _ { 1 } } + \frac { 1 } { x _ { 2 } } = - 1$$

Solve for x_1

$$x_{1}=-\frac{x_{2}}{x_{2}+1}$$

$$x_{2}\neq 0\text{ and }x_{2}\neq -1$$

Steps for Solving Linear Equation

Variable x_{1} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x_{1}x_{2}, the least common multiple of x_{1},x_{2}.

$$x_{2}+x_{1}=-x_{1}x_{2}$$

Add x_{1}x_{2} to both sides.

$$x_{2}+x_{1}+x_{1}x_{2}=0$$

Subtract x_{2} from both sides. Anything subtracted from zero gives its negation.

$$x_{1}+x_{1}x_{2}=-x_{2}$$

Combine all terms containing x_{1}.

$$\left(1+x_{2}\right)x_{1}=-x_{2}$$

The equation is in standard form.

$$\left(x_{2}+1\right)x_{1}=-x_{2}$$

Divide both sides by x_{2}+1.

$$\frac{\left(x_{2}+1\right)x_{1}}{x_{2}+1}=-\frac{x_{2}}{x_{2}+1}$$

Dividing by x_{2}+1 undoes the multiplication by x_{2}+1.

$$x_{1}=-\frac{x_{2}}{x_{2}+1}$$

Variable x_{1} cannot be equal to 0.

$$x_{1}=-\frac{x_{2}}{x_{2}+1}\text{, }x_{1}\neq 0$$

Solve for x_2

$$x_{2}=-\frac{x_{1}}{x_{1}+1}$$

$$x_{1}\neq 0\text{ and }x_{1}\neq -1$$

Steps for Solving Linear Equation

Variable x_{2} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x_{1}x_{2}, the least common multiple of x_{1},x_{2}.

$$x_{2}+x_{1}=-x_{1}x_{2}$$

Add x_{1}x_{2} to both sides.

$$x_{2}+x_{1}+x_{1}x_{2}=0$$

Subtract x_{1} from both sides. Anything subtracted from zero gives its negation.

$$x_{2}+x_{1}x_{2}=-x_{1}$$

Combine all terms containing x_{2}.

$$\left(1+x_{1}\right)x_{2}=-x_{1}$$

The equation is in standard form.

$$\left(x_{1}+1\right)x_{2}=-x_{1}$$

Divide both sides by x_{1}+1.

$$\frac{\left(x_{1}+1\right)x_{2}}{x_{1}+1}=-\frac{x_{1}}{x_{1}+1}$$

Dividing by x_{1}+1 undoes the multiplication by x_{1}+1.

$$x_{2}=-\frac{x_{1}}{x_{1}+1}$$

Variable x_{2} cannot be equal to 0.

$$x_{2}=-\frac{x_{1}}{x_{1}+1}\text{, }x_{2}\neq 0$$