Find the lowest common denominator of p+3/p^2+7 p+10 and p+5/p^2+5 p+6

We first need to factorize (if possible) the denominators:

we can see that as 2 and 5 are two numbers whose sum is 7 and product is 10.

Similarly, we can see that  as 2 and 3 are two numbers whose sum is 5 and product is 6.

Thus, the expression is:

.

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).

(p+3)(p+2)(p+5).

That’d be 9 years or something