You correctly rewrote 4^b as 22b in the denominator.

Question

ScanSolve AI Tutor · Accepted Answer

Your work is correct, Bonga🤍!

You have correctly simplified the expression.

You correctly rewrote $4^b$ as $2^{2b}$ in the denominator.
$\frac{2^b - 1}{2^{2b} - 1}$
You introduced the substitution $k = 2^b$ , which is a good way to simplify the appearance of the expression.
$\frac{k - 1}{k^2 - 1}$
You correctly factored the denominator $k^2 - 1$ using the difference of squares formula, $a^2 - c^2 = (a - c)(a + c)$ .
$\frac{k - 1}{(k - 1)(k + 1)}$
You correctly cancelled the common term $(k - 1)$ from the numerator and denominator.
$\frac{1}{k + 1}$
You substituted $k = 2^b$ back into the expression to get the final answer.
$\boxed{\frac{1}{2^b + 1}}$
✅ Correct!

Answer