Find the LCD of the given rational expressions.
-$$\frac { 7 } { x ^ { 2 } + 7 x + 10 } , \frac { 5 } { x ^ { 2 } + 6 x + 5 }$$
A) $( x + 2 ) ( x + 5 )$
B) $( x + 5 ) ( x + 1 )$
C) $( x + 2 ) ( x + 5 ) ( x + 1 )$
D) $( x - 2 ) ( x - 5 ) ( x + 1 )$

Question

Quizplus · Accepted Answer

To find the LCD, we need to factor the denominators and take the product of the highest power of each distinct factor.

Factorization of $x^2+7x+10$ gives $(x+2)(x+5)$.

Factorization of $x^2+6x+5$ gives $(x+5)(x+1)$.

So, the highest power of $x+2$ is 1, the highest power of $x+5$ is 1, and the highest power of $x+1$ is 1. Thus, the LCD is:

$$(x+2)(x+5)(x+1)$$

Therefore, the best choice is C.

Find the LCD of the Given Rational Expressions 7x2+7x+10,5x2+6x+5\frac { 7 } { x ^ { 2 } + 7 x + 10 } , \frac { 5 } { x ^ { 2 } + 6 x + 5 }x2+7x+107​,x2+6x+55​

Find the LCD of the Given Rational Expressions $\frac { 7 } { x ^ { 2 } + 7 x + 10 } , \frac { 5 } { x ^ { 2 } + 6 x + 5 }$