1/F = 1/20 + 1/9, what is F

1/F = 1/20 + 1/9, what is F

$$\\\small{\text{ $ \begin{array}{rcl} \dfrac{ 1 } { \rm{F} } &=& \dfrac{ 1 } { 20 } + \dfrac{ 1 } { 9 } \qquad | \qquad \cdot ( 20\cdot 9)\\\\ \dfrac{ 20\cdot 9 } { \rm{F} } &=& \dfrac{ 20\cdot 9 } { 20 } + \dfrac{ 20\cdot 9 } { 9 } \\\\ \dfrac{ 20\cdot 9 } { \rm{F} } &=& 9 + 20 \\\\ \dfrac{ 20\cdot 9 } { \rm{F} } &=& 29 \\\\ \dfrac{ 180 } { \rm{F} } &=& 29 \qquad | \qquad \cdot \rm{F}\\\\ \rm{F} \cdot 29 &=& 180 \qquad | \qquad :29\\\\ \rm{F} &=& \dfrac{ 180 } { 29 } \end{array} $}}$$

1/F  = 1/20  + 1/9 

1/F  = [29 / 180]     .....so......taking the reciprocals of both sides, we have

F  = [180/29]