(x+5)(x-6)
1) Considering that we have these two rational expressions:
[tex]\frac{1}{x+5}+\frac{1}{x-6}[/tex]
2) Since we have two different denominators, x+5 and x-6 then the least common denominator will be a simple product between them in this case:
[tex]\begin{gathered} \frac{1}{x+5}+\frac{1}{x-6}= \\ \frac{1(x-6)+1(x+5)}{(x+5)(x-6)}= \\ \frac{x-6+x+5}{(x+5)(x-6)}= \\ \frac{2x-1}{{\color{Red} (x+5)(x-6)}} \end{gathered}[/tex]
Note that after writing the Least Common Denominator (x-5)(x+6) we divide this by each original denominator and then multiply by the original numerator: 1 and then we add them up both.
3) Hence the least denominator is (x+5)(x-6) in red.
