x+3/(x^2+2x+2)^2
To simplify the given expression, we can start by breaking it down into parts. Let's analyze each component:
1. x: The variable x is already in its simplest form, so we can keep it as is.
2. (x^2 + 2x + 2)^2: This part of the expression involves a quadratic equation, which can be simplified using the FOIL method or by applying exponent rules. Let's expand it using the FOIL method:
(x^2 + 2x + 2) * (x^2 + 2x + 2)
= x^4 + 4x^3 + 4x^2 + 4x^3 + 8x^2 + 8x + 4x^2 + 8x + 8
= x^4 + 8x^3 + 16x^2 + 16x + 8
3. 3: This is a constant term and cannot be simplified any further.
Now that we have broken down the given expression, let's put it back together:
x + 3/(x^2 + 2x + 2)^2
= x + 3/(x^4 + 8x^3 + 16x^2 + 16x + 8)
This is the simplified form of the given expression.