Can use some help please!!!!

[MichaelGD3]

Hey, don't want the answer, but im I solving this the correct way?

FIND THE LCD OF THE RATIONAL EXPRESSION
1/x^2+7x+12 , 2/x^2+6x+9 and 5/x^2+2x-8

Answers I got are, (x+3)(x+4)(x+3)(x+3)(x+4(x-2) which one is the LCD? My teacher didn't really give a whole outline for this, so kinda confused, thanks

 

[Dr.Peterson]

Hey, don't want the answer, but im I solving this the correct way?

FIND THE LCD OF THE RATIONAL EXPRESSION
1/x^2+7x+12 , 2/x^2+6x+9 and 5/x^2+2x-8

Answers I got are, (x+3)(x+4)(x+3)(x+3)(x+4(x-2) which one is the LCD? My teacher didn't really give a whole outline for this, so kinda confused, thanks

I think you're saying that you want to find the least common denominator of the rational expressions 1/(x^2+7x+12) , 2/(x^2+6x+9), and 5/(x^2+2x-8). Those parentheses are required!

And you found that the denominators factor as (x+3)(x+4), (x+3)(x+3), and (x+4)(x-2). Those are correct. But they are not the LCD.

There are several ways to think about finding the LCD; one that I like is to start with one denominator, say (x+3)(x+4), and then ask yourself, what do I have to multiply by to make this also a multiple of (x+3)(x+3), and then again for (x+4)(x-2)?

Any thoughts?

If you have no textbook or notes explaining the process, try here:

9.3: Add and Subtract Rational Expressions

math.libretexts.org