[tex]\dfrac{p+3}{p^2+7p+10}=\dfrac{p+3}{p^2+5p+2p+10}=\dfrac{p+3}{p(p+5)+2(p+5)}=\dfrac{p+3}{(p+2)(p+5)}\\\\\dfrac{p+5}{p^2+5p+6}=\dfrac{p+5}{p^2+3p+2p+6}=\dfrac{p+5}{p(p+3)+2(p+3)}=\dfrac{p+5}{(p+3)(p+2)}\\\\\text{Lowest Common Denominator of}\ \dfrac{p+3}{p^2+7p+10}\ \text{and}\ \dfrac{p+5}{p^2+5p+6}\\\\\text{is}\ (p+5)(p+2)(p+3)\to\boxed{A.}[/tex]
