Solve 1/p+2/q=4/1

$$\frac { 1 } { p } + \frac { 2 } { q } = \frac { 4 } { 1 }$$

Solve for p

$$p=-\frac{q}{2\left(1-2q\right)}$$

$$q\neq 0\text{ and }q\neq \frac{1}{2}$$

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 pq, the least common multiple of p,q.

$$q+p\times 2=pq\times 4$$

Subtract pq\times 4 from both sides.

$$q+p\times 2-pq\times 4=0$$

Multiply -1 and 4 to get -4.

$$q+p\times 2-4pq=0$$

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

$$p\times 2-4pq=-q$$

Combine all terms containing p.

$$\left(2-4q\right)p=-q$$

Divide both sides by 2-4q.

$$\frac{\left(2-4q\right)p}{2-4q}=-\frac{q}{2-4q}$$

Dividing by 2-4q undoes the multiplication by 2-4q.

$$p=-\frac{q}{2-4q}$$

Divide -q by 2-4q.

$$p=-\frac{q}{2\left(1-2q\right)}$$

Variable p cannot be equal to 0.

$$p=-\frac{q}{2\left(1-2q\right)}\text{, }p\neq 0$$

Solve for q

$$q=-\frac{2p}{1-4p}$$

$$p\neq 0\text{ and }p\neq \frac{1}{4}$$

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.

$$q+p\times 2=pq\times 4$$

Subtract pq\times 4 from both sides.

$$q+p\times 2-pq\times 4=0$$

Multiply -1 and 4 to get -4.

$$q+p\times 2-4pq=0$$

Subtract p\times 2 from both sides. Anything subtracted from zero gives its negation.

$$q-4pq=-p\times 2$$

Combine all terms containing q.

$$\left(1-4p\right)q=-p\times 2$$

The equation is in standard form.

$$\left(1-4p\right)q=-2p$$

Divide both sides by 1-4p.

$$\frac{\left(1-4p\right)q}{1-4p}=-\frac{2p}{1-4p}$$

Dividing by 1-4p undoes the multiplication by 1-4p.

$$q=-\frac{2p}{1-4p}$$

Variable q cannot be equal to 0.

$$q=-\frac{2p}{1-4p}\text{, }q\neq 0$$