Solve 2=S/r_{1}+S/r_{2}

$$2 = \frac { S } { r _ { 1 } } + \frac { S } { r _ { 2 } }$$

Solve for S

$$S=\frac{2r_{1}r_{2}}{r_{1}+r_{2}}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by r_{1}r_{2}, the least common multiple of r_{1},r_{2}.

$$2r_{1}r_{2}=r_{2}S+r_{1}S$$

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

$$r_{2}S+r_{1}S=2r_{1}r_{2}$$

Combine all terms containing S.

$$\left(r_{2}+r_{1}\right)S=2r_{1}r_{2}$$

The equation is in standard form.

$$\left(r_{1}+r_{2}\right)S=2r_{1}r_{2}$$

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

$$\frac{\left(r_{1}+r_{2}\right)S}{r_{1}+r_{2}}=\frac{2r_{1}r_{2}}{r_{1}+r_{2}}$$

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

$$S=\frac{2r_{1}r_{2}}{r_{1}+r_{2}}$$

Solve for r_1

$$r_{1}=-\frac{Sr_{2}}{S-2r_{2}}$$

$$r_{2}\neq 0\text{ and }S\neq 0\text{ and }S\neq 2r_{2}$$

Steps for Solving Linear Equation

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

$$2r_{1}r_{2}=r_{2}S+r_{1}S$$

Subtract r_{1}S from both sides.

$$2r_{1}r_{2}-r_{1}S=r_{2}S$$

Combine all terms containing r_{1}.

$$\left(2r_{2}-S\right)r_{1}=r_{2}S$$

The equation is in standard form.

$$\left(2r_{2}-S\right)r_{1}=Sr_{2}$$

Divide both sides by 2r_{2}-S.

$$\frac{\left(2r_{2}-S\right)r_{1}}{2r_{2}-S}=\frac{Sr_{2}}{2r_{2}-S}$$

Dividing by 2r_{2}-S undoes the multiplication by 2r_{2}-S.

$$r_{1}=\frac{Sr_{2}}{2r_{2}-S}$$

Variable r_{1} cannot be equal to 0.

$$r_{1}=\frac{Sr_{2}}{2r_{2}-S}\text{, }r_{1}\neq 0$$