Question

What is the excluded value of x for x^2+3x+2/x^2+2x+1

Answer 1

Factoring we get 

(x + 2)(x + 1) / (x + 1)(x + 1)

The excluded value is x = -1

Answer 2

Answer:  The required value of x is $x=-1.$

Step-by-step explanation:  We are given to find the excluded value for the following rational expression:

$E=\dfrac{x^2+3x+2}{x^2+2x+1}.$

First, we need to factorize both numerator and denominator and then we should check the values of x for which the expression becomes undefined.

We have

$E\\\\=\dfrac{x^2+3x+2}{x^2+2x+1}\\\\\\=\dfrac{x^2+2x+x+2}{x^2+x+x+1}\\\\\\=\dfrac{x(x+2)+1(x+2)}{x(x+1)+1(x+1)}\\\\\\=\dfrac{(x+2)(x+1)}{(x+1)(x+1)}.$

Now, we can cancel $(x+1)$ by $(x+1)$, only if $x\neq 1,$ because

if $x=-1,$ then  $x+1=0$ and we cannot divide 0 by 0.

Therefore, if $x\neq 1,$ then

$E=\dfrac{(x+2)(x+1)}{(x+1)(x+1)}=\dfrac{x+2}{x+1},$

which is again well-defined because $x\neq -1$ and so the denominator never become zero.

Thus, the excluded value of x is  $x=-1.$