$\displaystyle \frac{2}{7}+\frac{7}{13}=\frac{[2]X[13]+[7]X[7]}{[7]X[13]}$
Im not sure how to multiply this out please show steps on how to do this. Thanks
Here is another way. To find inverse of 7 you need to solve $\displaystyle 7x\equiv 1(\bmod 18)$.
This is equivalent to $\displaystyle 7x\equiv 1 - 2\cdot 18(\bmod 18)\implies 7x\equiv -35(\bmod 18) \implies $$\displaystyle x\equiv -5(\bmod 18)\implies x\equiv 13(\bmod 18)$.