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

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

Solve for n

$$n=\frac{37787666611011727}{3320737444462996091}\approx 0.0113793$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{n}{3 + n} = 0.0037787666611011727$$

Variable n cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by n+3.

$$n=0.0037787666611011727\left(n+3\right)$$

Use the distributive property to multiply 0.0037787666611011727 by n+3.

$$n=0.0037787666611011727n+0.0113362999833035181$$

Subtract 0.0037787666611011727n from both sides.

$$n-0.0037787666611011727n=0.0113362999833035181$$

Combine n and -0.0037787666611011727n to get 0.9962212333388988273n.

$$0.9962212333388988273n=0.0113362999833035181$$

Divide both sides by 0.9962212333388988273.

$$n=\frac{0.0113362999833035181}{0.9962212333388988273}$$

Expand \frac{0.0113362999833035181}{0.9962212333388988273} by multiplying both numerator and the denominator by 10000000000000000000.

$$n=\frac{113362999833035181}{9962212333388988273}$$

Reduce the fraction \frac{113362999833035181}{9962212333388988273} to lowest terms by extracting and canceling out 3.

$$n=\frac{37787666611011727}{3320737444462996091}$$