Question

Find the LCD of$\frac{8}{y^2+12y+35},\frac{3y}{y^2+y-42}$.

Short answer

The LCD is$y^3+6y^2-37y-210$.

Step-by-step solution

Given Information 

The given expression is$\frac{8}{y^2+12y+35},\frac{3y}{y^2+y-42}$.

Factor the denominator of both expressions. 

The factored form of first denominator.

$y^2+12y+35=(y+5)(y+7)$

The factored form of second denominator.

$y^2+y-42=(y-6)(y+7)$

 Determine the common factors and from the remaining factors, multiply each of the denominator with appropriate factors.

The common factor is$(y+7)$.

Multiply common factor with other factors.

$=y^3+6y^2-37y-210$