Respuesta :
factoring we get
(x + 2)(x + 1) / (x + 1)(x + 1)
The excluded value is x = -1
(x + 2)(x + 1) / (x + 1)(x + 1)
The excluded value is x = -1
Answer: The required value of x is [tex]x=-1.[/tex]
Step-by-step explanation: We are given to find the excluded value for the following rational expression:
[tex]E=\dfrac{x^2+3x+2}{x^2+2x+1}.[/tex]
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
[tex]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)}.[/tex]
Now, we can cancel [tex](x+1)[/tex] by [tex](x+1)[/tex], only if [tex]x\neq 1,[/tex] because
if [tex]x=-1,[/tex] then [tex]x+1=0[/tex] and we cannot divide 0 by 0.
Therefore, if [tex]x\neq 1,[/tex] then
[tex]E=\dfrac{(x+2)(x+1)}{(x+1)(x+1)}=\dfrac{x+2}{x+1},[/tex]
which is again well-defined because [tex]x\neq -1[/tex] and so the denominator never become zero.
Thus, the excluded value of x is [tex]x=-1.[/tex]
