We first need to factorize (if possible) the denominators:
we can see that [tex]p^2+7p+10=(p+2)(p+5)[/tex] as 2 and 5 are two numbers whose sum is 7 and product is 10.
Similarly, we can see that [tex]p^2+5p+6=(p+3)(p+2)[/tex] as 2 and 3 are two numbers whose sum is 5 and product is 6.
Thus, the expression is:
[tex]\displaystyle{ \frac{p+3}{(p+2)(p+5)} + \frac{p+5}{(p+3)(p+2)} [/tex].
Now to make the denominators equal, but to also keep them as small as possible, the common denominator must be (p+3)(p+2)(p+5).
Answer: (p+3)(p+2)(p+5).
