Question

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

Answer 1

Answer:

The answer you are looking for is (p+3)(p+2)(p+5).

Answer 2

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

we can see that $p^2+7p+10=(p+2)(p+5)$ as 2 and 5 are two numbers whose sum is 7 and product is 10.


Similarly, we can see that $p^2+5p+6=(p+3)(p+2)$ as 2 and 3 are two numbers whose sum is 5 and product is 6.

Thus, the expression is:

$\displaystyle{ \frac{p+3}{(p+2)(p+5)} + \frac{p+5}{(p+3)(p+2)}$.


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).