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QUESTION IMAGE

guided practice type the numerator in the left blank and the denominato…

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:

$2y - 1$