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=(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\\\\=(x^2+3x+2)/(x^2+2x+1)\\\\\\=(x^2+2x+x+2)/(x^2+x+x+1)\\\\\\=(x(x+2)+1(x+2))/(x(x+1)+1(x+1))\\\\\\=((x+2)(x+1))/((x+1)(x+1)).`

Now, we can cancel
`(x+1)` by
`(x+1)`, only if
`x\\eq 1,` because

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

Therefore, if
`x\\eq 1,` then

`E=((x+2)(x+1))/((x+1)(x+1))=(x+2)/(x+1),`

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

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