which expression is equivalent to the following complex fraction?\n$\frac{1+\frac{1}{y}}{1…

which expression is equivalent to the following complex fraction?\n$\frac{1+\frac{1}{y}}{1 - \frac{1}{y}}$\n$\frac{(y + 1)(y - 1)}{y^{2}}$\n$\frac{y + 1}{y - 1}$\n$\frac{y - 1}{y + 1}$\n$\frac{y^{2}}{(y + 1)(y - 1)}$
Answer
Explanation:
Step1: Simplify numerator and denominator
The numerator $1+\frac{1}{y}=\frac{y + 1}{y}$, and the denominator $1-\frac{1}{y}=\frac{y-1}{y}$.
Step2: Rewrite the complex - fraction
The complex fraction $\frac{1+\frac{1}{y}}{1 - \frac{1}{y}}$ becomes $\frac{\frac{y + 1}{y}}{\frac{y-1}{y}}$.
Step3: Divide by a fraction
Dividing by a fraction is the same as multiplying by its reciprocal. So $\frac{\frac{y + 1}{y}}{\frac{y-1}{y}}=\frac{y + 1}{y}\times\frac{y}{y-1}$.
Step4: Simplify the expression
The $y$ terms cancel out, and we get $\frac{y + 1}{y-1}$.
Answer:
$\frac{y + 1}{y-1}$