which expression is equivalent to the following complex fraction?

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

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

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

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

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

Question

which expression is equivalent to the following complex fraction?

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

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

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

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

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Complex Fractions" ], "new_concepts": [], "current_concepts": [ "Complex Fractions" ] } ## Simplify the numerator and denominator $$ \begin{aligned} 1 + \frac{1}{y} &= \frac{y + 1}{y} \ 1 - \frac{1}{y} &= \frac{y - 1}{y} \end{aligned} $$ ## Divide the simplified expressions $$ \frac{\frac{y + 1}{y}}{\frac{y - 1}{y}} = \frac{y + 1}{y} \cdot \frac{y}{y - 1} = \frac{y + 1}{y - 1} $$

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

(B) $\frac{y+1}{y-1}$

(C) $\frac{y-1}{y+1}$

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

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Complex Fractions" ] }

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QUESTION IMAGE

Question

Explanation:

Simplify the numerator and denominator

Divide the simplified expressions

Answer: