Question

What is the LCD of `(p+3)/(p^2 + 7p + 10)` and `(p+5)/(p^2+5p+6)`?

Answer 1

LCD is `(p+2)(p+3)(p+5)=p^3+10p^2+31p+30`

Explanation:

To find LCD of `(p+3)/(p^2+7p+10)` and `(p+5)/(p^2+5p+6)`

We should first factorize each denominator and then find LCM of denominators.

As `p^2+7p+10=p^2+5p+2p+10=p(p+5)+2(p+5)=(p+2)(p+5)`

and `p^2+5p+6=p^2+3p+2p+6=p(p+3)+2(p+3)=(p+2)(p+3)`

Common factor is `(p+2)`, hence this comes only once in LCD, while remaining factors are taken as it is and then they are multipled. Hence

LCD is `(p+2)(p+3)(p+5)=(p+3)(p+2)(p+5)`

= `(p+3)(p^2+7p+10)` - (this product is already given above)

= `p^3+7p^2+10p+3p^2+21p+30`

= `p^3+10p^2+31p+30`