Write the simplified fraction [(x+2)^2*(x+1)/(x+1)^2]*[(x^2+2x+1)/(x^2+3x+2)]

First, we'll write the numerators and denominators as
distinct factors. For this reason, we'll determine the roots of the 2nd
numerator:

x^2 + 2x + 1 =
0

We'll recognize the perfect
square:

(x+1)^2 = 0

Now, we'll
determine the roots of the denominator of the 2nd
fraction:

x^2 + 3x + 2 =
0

We'll apply quadratic
formula:

x1 = [-3+sqrt(9 -
8)]/2

x1 = (-3+1)/2

x1 =
-1

x2 = (-3-1)/2

x2 =
-2

The equation will be written
as:

x^2 + 3x + 2 = (x + 1)(x +
2)

We'll re-write the factorised
expression:

[(x+2)^2*(x+1)/(x+1)^2]*[(x+1)^2/(x + 1)(x +
2)]

We'll cancel common
factors:

[(x+2)^2*(x+1)/(x+1)^2]*[(x+1)^2/(x + 1)(x + 2)] =
x + 2

The  requested simplified result of the
given expression is: (x+2)