Answer: The lowest common denominator of the given fractions is [tex](p+2)(p+3)(p+5).[/tex]
Step-by-step explanation: We are given to find the lowest common denominator of the following fractions :
[tex]F_1=\dfrac{p+3}{p^2+7p+10},\\\\\\F_2=\dfrac{p+5}{p^2+5p+6}.[/tex]
To find the lowest common denominator, we need to factorize the denominators of both the fractions and take the L.C.M. of them.
We have
[tex]F_1=\dfrac{p+3}{p^2+7p+10}=\dfrac{p+3}{p^2+5p+2p+10}=\dfrac{p+3}{(p+2)(p+5)},\\\\\\F_2=\dfrac{p+5}{p^2+5p+6}=\dfrac{p+5}{p^2+3p+2p+6}=\dfrac{p+5}{(p+2)(p+3)}.[/tex]
Now, the L.C.M. of the denominators is given by
[tex]L.C.M.\{(p+2)(p+5),(p+2)(p+3)\}=(p+2)(p+3)(p+5).[/tex]
Thus, the lowest common denominator of the given fractions is [tex](p+2)(p+3)(p+5).[/tex]
