Respuesta :
Answer: The required lowest common denominator of both the fractions is [tex]x^3+10x^2+31x+30.[/tex]
Step-by-step explanation: We are given to find the lowest common denominator of the following two fractions :
[tex]f_1=\dfrac{p+3}{p^2+7p+10},~~~f_2=\dfrac{p+5}{p^2+5p+6}.[/tex]
After factorizing the denominators, the fractions become
[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]
Therefore, the lowest common denominator of both the fractions is
[tex]L.C.M.((x+2)(x+5),(x+2)(x+3))\\\\=(x+2)(x+3)(x+5)\\\\=(x^2+5x+6)(x+5)\\\\=x^3+5x^2+6x+5x^2+25x+30\\\\=x^3+10x^2+31x+30.[/tex]
Thus, the required lowest common denominator of both the fractions is [tex]x^3+10x^2+31x+30.[/tex]
