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

Answer 1

First let us factor the denominators:

p²+7p+10 = (p+2)(p+5)
p²+5p+6 = (p+2)(p+3)

So the LCD is (p+2)(p+3)(p+5) = (p²+5p+6)(p+5) = p³ + 10p² + 31p + 30

ETA: please respect the order of operations -- place parentheses around expressions which are supposed to be grouped as a single term. In this case, you should use (p+3)/(p²+7p+10) and (p+5)/(p²+5p+6). What you actually wrote would be interpreted as 8p + (3/p²) + 10 and 6p + (5/p²) + 6 under the order of operations.