Question

guided practice
type the numerator in the left blank and the denominator in the right blank. then click or tap done.
use the ^ symbol (shift+6 on the keyboard) to signify an exponent. for example, for 2 to the third power, enter 2^3.
simplify.
\\(\frac{2^y - 1}{1 - \frac{y}{2^{y - 1}}}\\)

Explanation:

Step1: Rewrite the complex fraction

$\frac{2y - 1}{\frac{1}{2y - 1}} = (2y - 1) \div \frac{1}{2y - 1}$

Step2: Divide by reciprocal

$(2y - 1) \times (2y - 1) = (2y - 1)^2$

Step3: Expand the square

$(2y)^2 - 2 \times 2y \times 1 + 1^2 = 4y^2 - 4y + 1$

Wait, correction: The original expression is $\frac{2y - 1}{\frac{1}{2y - 1}}$, which is $(2y - 1) \times (2y - 1) = (2y - 1)^2 = 4y^2 - 4y + 1$. Yes, that's correct.

Final Answer: $4y^2 - 4y + 1$

Answer:

$2y - 1$