Show all your work.
Simplify :
x^2 +3x+2 / x+2

Question

Show all your work.
Simplify :
x^2 +3x+2 / x+2

anonymous · Answer

Find the LCD for step #1

zolock · Answer

is there another way ti do this.

anonymous · Answer

the first term has a denominator of 1 and the second term has one of 1(x+2)

anonymous · Answer

since they both have 1 you don't have to do anything with it, but since only the second term has a denominator of (x+2), you have to multiply top and bottom of the first term by (x+2)

mathstudent55 · Answer

First, factor the numerator.

anonymous · Answer

we are unsure of what the numerator for any term is

anonymous · Answer

but yes that would be wise

mathstudent55 · Answer

$\dfrac{x^2 + 3x + 2}{x + 2} $

First, factor the numerator. Try one factor of x + 2, and find the other factor. If you can factor that way, then you can cancel out the common factor. If you can't factor the numerator and get one factor of x + 2, then you can't simplify the fraction because the only factor available in the denominator for reducing is x + 2.

zolock · Answer

then

mathstudent55 · Answer

Have you factored the numerator?

zolock · Answer

(x+2)(x+1)

mathstudent55 · Answer

Great.
Now let's write that in the fraction.

$\dfrac{x^2 + 3x + 2}{x + 2} $

$=\dfrac{(x + 2)(x + 1)}{x + 2}$    We are up to here now.

Do you see a common factor in the numerator and denominator?

zolock · Answer

yes

mathstudent55 · Answer

Good.
Now you divide both the numerator and the denominator by the common factor.

mathstudent55 · Answer

What do you get?

zolock · Answer

i get x +1

mathstudent55 · Answer

Correct.

$=\dfrac{\cancel{\color{red}{(x + 2)}}(x + 1)}{\cancel{\color{red}{x + 2}}}$

$= x + 1 $

zolock · Answer

thank you very much mathstudent55

mathstudent55 · Answer

You're welcome.