Final answer:
Rationalize the denominator and simplify the expression (Sqrt(A+1) - 2) / (Sqrt(A+1) + 2), we multiply both the numerator and the denominator by the conjugate. Simplifying further, we get (A - 3)/(A - 4).
Step-by-step explanation:
To rationalize the denominator and simplify the expression, we need to multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of Sqrt(A+1) + 2 is Sqrt(A+1) - 2. Therefore, we multiply the expression by (Sqrt(A+1) - 2)/(Sqrt(A+1) - 2).
Expanding the numerator and denominator, we get ((Sqrt(A+1) - 2)*(Sqrt(A+1) - 2))/(Sqrt(A+1) + 2)*(Sqrt(A+1) - 2)). Simplifying further, we get ((A+1) - 4*Sqrt(A+1) + 4)/(A - 4).
Finally, we can simplify the expression by dividing the numerator and the denominator by their common factors. The simplified expression is (A - 3)/(A - 4).