Definition:Common Denominator

Definition
Consider the expression:
 * $\dfrac a b + \dfrac c d$

where $a$, $b$, $c$ and $d$ are any expressions whatsoever which evaluate to a number such that neither $c$ nor $d$ evaluate to zero.

In order to be able to perform the required addition, it is necessary to put the expressions $\dfrac a b$ and $\dfrac c d$ over a common denominator.

Hence the operation is:
 * to multiply both the numerator (top) and denominator (bottom) of $\dfrac a b$ by $d$

and in the same operation:
 * to multiply both the numerator (top) and denominator (bottom) of $\dfrac c d$ by $b$

in order to obtain the expression:
 * $\dfrac {a d} {b d} + \dfrac {b c} {b d}$

Hence one may perform the operation as:
 * $\dfrac {a d + b c} {b d}$

and either evaluate or simplify appropriately.