Answer:
B.
Explanation:
The given expression is
[tex]\frac{x+2}{4x^2+5x+1}\cdot\frac{4x+1}{x^2-4}[/tex]
Then, we can factorize the denominators are
4x² + 5x + 1 = (4x + 1)(x + 1)
x² - 4 = (x + 2)(x - 2)
So, the expression is equal to
[tex]\frac{x+2}{(4x+1)(x+1)}\cdot\frac{4x+1}{(x+2)(x-2)}[/tex]
Then, multiply the expression and simplify
[tex]\begin{gathered} \frac{(x+2)(4x+1)}{(4x+1)(x+1)(x+2)(x-2)} \\ \\ \frac{1}{(x+1)(x-2)} \end{gathered}[/tex]
Therefore, the answer is B.
