Hi folks,

Starting with 6 field axioms, I'm proving a sequence of 15 algebraic laws.

Number 13 in my list is: $\displaystyle (ab) + (cd) = (ad + bc)/(bd)$

Using the axioms and prior theorems:

$\displaystyle a\cdot 1/b + c\cdot 1/d$

$\displaystyle a\cdot 1/b\cdot d\cdot 1/d + c\cdot 1/d\cdot b\cdot 1/b$

$\displaystyle ad\cdot 1/b\cdot 1/d + bc\cdot 1/b\cdot 1/d$

$\displaystyle (ad +bc)\cdot 1/b\cdot 1/d$

I'm stuck here. I'm not seeing how to get from $\displaystyle 1/b\cdot 1/d$ to $\displaystyle 1/bd$ thus allowing the final step achieving the RHS. Unfortunately, the general case $\displaystyle (a/b)(c/d) = (ac)/(bd)$ is the next theorem in the list, and so, not available.

If you can provide a hint, I'd appreciate it.

Thanks,

Scott