Solve 2/r=7/p-1/q

$$\frac { 2 } { r } = \frac { 7 } { p } - \frac { 1 } { q }$$

Solve for p

$$p=\frac{7qr}{2q+r}$$

$$q\neq 0\text{ and }r\neq 0\text{ and }r\neq -2q$$

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 pqr, the least common multiple of r,p,q.

$$pq\times 2=qr\times 7-pr$$

Add pr to both sides.

$$pq\times 2+pr=qr\times 7$$

Combine all terms containing p.

$$\left(q\times 2+r\right)p=qr\times 7$$

The equation is in standard form.

$$\left(2q+r\right)p=7qr$$

Divide both sides by 2q+r.

$$\frac{\left(2q+r\right)p}{2q+r}=\frac{7qr}{2q+r}$$

Dividing by 2q+r undoes the multiplication by 2q+r.

$$p=\frac{7qr}{2q+r}$$

Variable p cannot be equal to 0.

$$p=\frac{7qr}{2q+r}\text{, }p\neq 0$$

Solve for q

$$q=-\frac{pr}{2p-7r}$$

$$p\neq 0\text{ and }r\neq 0\text{ and }r\neq \frac{2p}{7}$$

Steps for Solving Linear Equation

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

$$pq\times 2=qr\times 7-pr$$

Subtract qr\times 7 from both sides.

$$pq\times 2-qr\times 7=-pr$$

Multiply -1 and 7 to get -7.

$$pq\times 2-7qr=-pr$$

Combine all terms containing q.

$$\left(p\times 2-7r\right)q=-pr$$

The equation is in standard form.

$$\left(2p-7r\right)q=-pr$$

Divide both sides by 2p-7r.

$$\frac{\left(2p-7r\right)q}{2p-7r}=-\frac{pr}{2p-7r}$$

Dividing by 2p-7r undoes the multiplication by 2p-7r.

$$q=-\frac{pr}{2p-7r}$$

Variable q cannot be equal to 0.

$$q=-\frac{pr}{2p-7r}\text{, }q\neq 0$$