1/12 + 1/x = 1/6.86

1/12 + 1/x = 1/6.86

$\begin{array}{rcll} \frac{1}{12} + \frac{1}{x} &=& \frac{1}{6.86} \qquad | \qquad - \frac{1}{12} \\\\ \frac{1}{x} &=& \frac{1}{6.86} - \frac{1}{12} \\\\ \frac{1}{x} &=& \frac{1}{6.86}\cdot \frac{12}{12} - \frac{1}{12}\cdot \frac{6.86}{6.86} \\\\ \frac{1}{x} &=& \frac{1\cdot 12 - 1 \cdot 6.86}{6.86\cdot 12 } \\\\ x &=& \frac{6.86\cdot 12 }{1\cdot 12 - 1 \cdot 6.86} \\\\ x &=& \frac{6.86\cdot 12 }{12 - 6.86} \\\\ x &=& \frac{82.32}{5.14} \\\\ \mathbf{x} &\mathbf{=}& \mathbf{16.0155642023} \\\\ \end{array}$

Solve for x:
1/12+1/x = 0.145773

0.145773 = 50/343:
1/12+1/x = 50/343

Bring 1/12+1/x together using the common denominator 12 x:
(x+12)/(12 x) = 50/343

Cross multiply:
343 (x+12) = 600 x

Expand out terms of the left hand side:
343 x+4116 = 600 x

Subtract 600 x+4116 from both sides:
-257 x = -4116

Divide both sides by -257:
Answer: | 
| x = 4116/257