Final answer:
To simplify the expression (x + 2)/(4x^2 + 5x + 1) × (4x + 1)/(x^2 - 1), expand the numerator and denominator, then cancel out common factors.
Step-by-step explanation:
Step 1:
Expand the expression and multiply both numerators together to get:
(x + 2)(4x + 1)
Step 2:
Expand the denominator and multiply both denominators together to get:
(4x^2 + 5x + 1)(x^2 - 1)
Step 3:
Now we can simplify by canceling common factors in the numerator and denominator.
In this case, we can cancel out the factor (x + 2) and the factor (x - 1).
So the simplified expression is:
(4x + 1)(x + 2)/(4x^2 + 5x + 1)(x^2 - 1)