This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Rewrite the denominator using exponent rules. The denominator is 4^b - 1. We can express 4 as 2^2. 4^b - 1 = (2^2)^b - 1 Using the exponent rule (x^m)^n = x^mn, we get: (2^2)^b - 1 = 2^2b - 1 This can also be written as (2^b)^2 - 1. Step 2: Apply the difference of squares formula to the denominator. The difference of squares formula is a^2 - c^2 = (a - c)(a + c). Here, a = 2^b and c = 1. (2^b)^2 - 1^2 = (2^b - 1)(2^b + 1) Step 3: Substitute the factored denominator back into the original expression. (2^b - 1)/(4^b - 1) = (2^b - 1)/((2^b - 1)(2^b + 1)) Step 4: Cancel out the common term in the numerator and denominator. Assuming 2^b - 1 ≠ 0, we can cancel (2^b - 1) from both the numerator and the denominator. (1)/(2^b + 1) The simplified expression is: (1)/(2^b + 1) Send me the next one 📸