Solve 1/p+1/q=1/sqrt{8040}

$$\frac { 1 } { p } + \frac { 1 } { q } = \frac { 1 } { \sqrt { 8040 } }$$

Solve for p

$$p=-\frac{2\sqrt{2010}q}{-q+2\sqrt{2010}}$$

$$q\neq 0\text{ and }q\neq 2\sqrt{2010}$$

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 pq, the least common multiple of p,q.

$$q+p=\frac{1}{4020}pq\times 2010^{\frac{1}{2}}$$

Subtract \frac{1}{4020}pq\times 2010^{\frac{1}{2}} from both sides.

$$q+p-\frac{1}{4020}pq\times 2010^{\frac{1}{2}}=0$$

Reorder the terms.

$$p+q-\frac{1}{4020}\sqrt{2010}pq=0$$

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

$$p-\frac{1}{4020}\sqrt{2010}pq=-q$$

Combine all terms containing p.

$$\left(1-\frac{1}{4020}\sqrt{2010}q\right)p=-q$$

The equation is in standard form.

$$\left(-\frac{\sqrt{2010}q}{4020}+1\right)p=-q$$

Divide both sides by 1-\frac{1}{4020}\sqrt{2010}q.

$$\frac{\left(-\frac{\sqrt{2010}q}{4020}+1\right)p}{-\frac{\sqrt{2010}q}{4020}+1}=-\frac{q}{-\frac{\sqrt{2010}q}{4020}+1}$$

Dividing by 1-\frac{1}{4020}\sqrt{2010}q undoes the multiplication by 1-\frac{1}{4020}\sqrt{2010}q.

$$p=-\frac{q}{-\frac{\sqrt{2010}q}{4020}+1}$$

Divide -q by 1-\frac{1}{4020}\sqrt{2010}q.

$$p=-\frac{4020q}{-\sqrt{2010}q+4020}$$

Variable p cannot be equal to 0.

$$p=-\frac{4020q}{-\sqrt{2010}q+4020}\text{, }p\neq 0$$

Solve for q

$$q=-\frac{2\sqrt{2010}p}{-p+2\sqrt{2010}}$$

$$p\neq 0\text{ and }p\neq 2\sqrt{2010}$$

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 pq, the least common multiple of p,q.

$$q+p=\frac{1}{4020}pq\times 2010^{\frac{1}{2}}$$

Subtract \frac{1}{4020}pq\times 2010^{\frac{1}{2}} from both sides.

$$q+p-\frac{1}{4020}pq\times 2010^{\frac{1}{2}}=0$$

Reorder the terms.

$$p+q-\frac{1}{4020}\sqrt{2010}pq=0$$

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

$$q-\frac{1}{4020}\sqrt{2010}pq=-p$$

Combine all terms containing q.

$$\left(1-\frac{1}{4020}\sqrt{2010}p\right)q=-p$$

The equation is in standard form.

$$\left(-\frac{\sqrt{2010}p}{4020}+1\right)q=-p$$

Divide both sides by 1-\frac{1}{4020}\sqrt{2010}p.

$$\frac{\left(-\frac{\sqrt{2010}p}{4020}+1\right)q}{-\frac{\sqrt{2010}p}{4020}+1}=-\frac{p}{-\frac{\sqrt{2010}p}{4020}+1}$$

Dividing by 1-\frac{1}{4020}\sqrt{2010}p undoes the multiplication by 1-\frac{1}{4020}\sqrt{2010}p.

$$q=-\frac{p}{-\frac{\sqrt{2010}p}{4020}+1}$$

Divide -p by 1-\frac{1}{4020}\sqrt{2010}p.

$$q=-\frac{4020p}{-\sqrt{2010}p+4020}$$

Variable q cannot be equal to 0.

$$q=-\frac{4020p}{-\sqrt{2010}p+4020}\text{, }q\neq 0$$