Solve 1/x=1/x1+1/x2

$$\frac{ 1 }{ x } = \frac{ 1 }{ x1 } + \frac{ 1 }{ x2 }$$

Solve for x

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

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

Steps for Solving Linear Equation

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

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

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

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by x_{1}+x_{2}.

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

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

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

Variable x cannot be equal to 0.

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

Solve for x_1

$$x_{1}=-\frac{xx_{2}}{x-x_{2}}$$

$$x_{2}\neq 0\text{ and }x\neq 0\text{ and }x\neq x_{2}$$

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 xx_{1}x_{2}, the least common multiple of x,x_{1},x_{2}.

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

Subtract xx_{1} from both sides.

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

Combine all terms containing x_{1}.

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

Divide both sides by -x+x_{2}.

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

Dividing by -x+x_{2} undoes the multiplication by -x+x_{2}.

$$x_{1}=\frac{xx_{2}}{x_{2}-x}$$

Variable x_{1} cannot be equal to 0.

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