Solve frac{sqrt{3}+2}{1}=p/q

$$\frac{ \sqrt{ 3 } +2 }{ 1 } = \frac{ p }{ q }$$

Solve for q

$$q=\left(2-\sqrt{3}\right)p$$

$$p\neq 0$$

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.

$$q\left(\sqrt{3}+2\right)=p$$

Use the distributive property to multiply q by \sqrt{3}+2.

$$q\sqrt{3}+2q=p$$

Combine all terms containing q.

$$\left(\sqrt{3}+2\right)q=p$$

Divide both sides by \sqrt{3}+2.

$$\frac{\left(\sqrt{3}+2\right)q}{\sqrt{3}+2}=\frac{p}{\sqrt{3}+2}$$

Dividing by \sqrt{3}+2 undoes the multiplication by \sqrt{3}+2.

$$q=\frac{p}{\sqrt{3}+2}$$

Divide p by \sqrt{3}+2.

$$q=-\left(\sqrt{3}-2\right)p$$

Variable q cannot be equal to 0.

$$q=-\left(\sqrt{3}-2\right)p\text{, }q\neq 0$$

Solve for p

$$p=\left(\sqrt{3}+2\right)q$$

$$q\neq 0$$