Solve frac{sqrt{8}+2}{1}=p/q

$$\frac { \sqrt { 8 } + 2 } { 1 } = \frac { p } { q }$$

Solve for q

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

$$p\neq 0$$

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 q.

$$q\left(\sqrt{8}+2\right)=p$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$q\left(2\sqrt{2}+2\right)=p$$

Use the distributive property to multiply q by 2\sqrt{2}+2.

$$2q\sqrt{2}+2q=p$$

Combine all terms containing q.

$$\left(2\sqrt{2}+2\right)q=p$$

Divide both sides by 2\sqrt{2}+2.

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

Dividing by 2\sqrt{2}+2 undoes the multiplication by 2\sqrt{2}+2.

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

Divide p by 2\sqrt{2}+2.

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

Variable q cannot be equal to 0.

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

Solve for p

$$p=2\left(\sqrt{2}+1\right)q$$

$$q\neq 0$$