Question

How do you combine `4/(a^2 + 12a +27) + 5/(a^2 +10a +21)`?

Answer 1

Since `a^2+12a+27 = (a+3)(a+9)`
and `a^2+10a+21 = (a+3)(a+7)`

The Least Common Divisor needed to combine these two terms is
`(a+3)(a+7)(a+9)`

`4/(a^2+12a+27) + 5/(a^2+10a+21)`

`= (4(a+7) + 5(a+9))/((a+3)(a+7)(a+9))`

`= (9a +73)/((a+3)(a+7)(a+9))`