Question

Find the lowest common denominator of p+3/p2+7p+10 and p5/p2+5p+6

Answer 1

(P+1)(p+2)(p+5) is LCM

Answer 2

Answer: The required lowest common denominator of both the fractions is
`x^3+10x^2+31x+30.`

Step-by-step explanation: We are given to find the lowest common denominator of the following two fractions :

`f_1=(p+3)/(p^2+7p+10),~~~f_2=(p+5)/(p^2+5p+6).`

After factorizing the denominators, the fractions become

`f_1=(p+3)/(p^2+7p+10)=(p+3)/(p^2+5p+2p+10)=(p+3)/((p+2)(p+5)),\\\\\\f_2=(p+5)/(p^2+5p+6)=(p+5)/(p^2+3p+2p+6)=(p+5)/((p+2)(p+3)).`

Therefore, the lowest common denominator of both the fractions is

`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.`

Thus, the required lowest common denominator of both the fractions is
`x^3+10x^2+31x+30.`