Addition of Fractions

Theorem
Let $a, b, c, d \in \Z$ such that $b d \ne 0$.

Then:


 * $\dfrac a b + \dfrac c d = \dfrac {a D + B c} {\lcm \set {b, d} }$

where:
 * $B = \dfrac b {\gcd \set {b, d} }$


 * $D = \dfrac d {\gcd \set {b, d} }$


 * $\lcm$ denotes lowest common multiple


 * $\gcd$ denotes greatest common divisor.