Solve 1/p+1/q=2/R

$$\frac { 1 } { p } + \frac { 1 } { q } = \frac { 2 } { R }$$

Solve for R

$$R=\frac{2pq}{p+q}$$

$$p\neq 0\text{ and }q\neq 0\text{ and }p\neq -q$$

Steps for Solving Linear Equation

Variable R cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by Rpq, the least common multiple of p,q,R.

$$Rq+Rp=pq\times 2$$

Reorder the terms.

$$Rp+Rq=2pq$$

Combine all terms containing R.

$$\left(p+q\right)R=2pq$$

Divide both sides by q+p.

$$\frac{\left(p+q\right)R}{p+q}=\frac{2pq}{p+q}$$

Dividing by q+p undoes the multiplication by q+p.

$$R=\frac{2pq}{p+q}$$

Variable R cannot be equal to 0.

$$R=\frac{2pq}{p+q}\text{, }R\neq 0$$

Solve for p

$$p=-\frac{Rq}{R-2q}$$

$$q\neq 0\text{ and }R\neq 0\text{ and }q\neq \frac{R}{2}$$

Steps for Solving Linear Equation

Variable p cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by Rpq, the least common multiple of p,q,R.

$$Rq+Rp=pq\times 2$$

Subtract pq\times 2 from both sides.

$$Rq+Rp-pq\times 2=0$$

Multiply -1 and 2 to get -2.

$$Rq+Rp-2pq=0$$

Subtract Rq from both sides. Anything subtracted from zero gives its negation.

$$Rp-2pq=-Rq$$

Combine all terms containing p.

$$\left(R-2q\right)p=-Rq$$

Divide both sides by R-2q.

$$\frac{\left(R-2q\right)p}{R-2q}=-\frac{Rq}{R-2q}$$

Dividing by R-2q undoes the multiplication by R-2q.

$$p=-\frac{Rq}{R-2q}$$

Variable p cannot be equal to 0.

$$p=-\frac{Rq}{R-2q}\text{, }p\neq 0$$