Question

Find the lowest common denominator of p+3/p2+7p+10 and p+5/ p2+5p+6 A. (p + 5)(p + 2)(p + 3)

B. (p + 5)(p + 3)
C. (p + 2)2
D. (p + 2)

Answer 1

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