Solve n/3+n=frac{sqrt{3}}{8}

$$\frac{ n }{ 3+n } = \frac{ \sqrt{ 3 } }{ 8 }$$

Solve for n

$$n=\frac{24\sqrt{3}+9}{61}\approx 0.829003596$$

Steps for Solving Linear Equation

Variable n cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by 8\left(n+3\right), the least common multiple of 3+n,8.

$$8n=\left(n+3\right)\sqrt{3}$$

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

$$8n=n\sqrt{3}+3\sqrt{3}$$

Subtract n\sqrt{3} from both sides.

$$8n-n\sqrt{3}=3\sqrt{3}$$

Reorder the terms.

$$-\sqrt{3}n+8n=3\sqrt{3}$$

Combine all terms containing n.

$$\left(-\sqrt{3}+8\right)n=3\sqrt{3}$$

The equation is in standard form.

$$\left(8-\sqrt{3}\right)n=3\sqrt{3}$$

Divide both sides by -\sqrt{3}+8.

$$\frac{\left(8-\sqrt{3}\right)n}{8-\sqrt{3}}=\frac{3\sqrt{3}}{8-\sqrt{3}}$$

Dividing by -\sqrt{3}+8 undoes the multiplication by -\sqrt{3}+8.

$$n=\frac{3\sqrt{3}}{8-\sqrt{3}}$$

Divide 3\sqrt{3} by -\sqrt{3}+8.

$$n=\frac{24\sqrt{3}+9}{61}$$