Question

which expression is equivalent to the following complex fraction?

\\\frac{1+\frac{1}{y}}{1-\frac{1}{y}}\\

\\\frac{(y+1)(y-1)}{y^2}\\

\\\frac{y+1}{y-1}\\

\\\frac{y-1}{y+1}\\

\\\frac{y^2}{(y+1)(y-1)}\\

Explanation:

Simplify the numerator and denominator

$$
LATEXBLOCK0
$$

Divide the simplified expressions

$$ \frac{\frac{y + 1}{y}}{\frac{y - 1}{y}} = \frac{y + 1}{y} \cdot \frac{y}{y - 1} = \frac{y + 1}{y - 1} \quad (y eq 0, y eq 1) $$

Answer:

• (A) \(\frac{(y+1)(y-1)}{y^2}\)
• (B) \(\frac{y+1}{y-1}\) (Correct answer)
• (C) \(\frac{y-1}{y+1}\)
• (D) \(\frac{y^2}{(y+1)(y-1)}\)