Which expression is equivalent to $\frac{\frac{1}{y}+\frac{1}{x}}{\frac{3}{x y}}$ ?
Assume $x
eq 0, y
eq 0$, and $x
eq-y$.
Choose 1 answer:
(A) $\frac{x+y}{3}$
(B) $\frac{3}{x+y}$
(c) 3
(D) $\frac{1}{3}$

Question

Which expression is equivalent to $\frac{\frac{1}{y}+\frac{1}{x}}{\frac{3}{x y}}$ ?
Assume $x 
eq 0, y 
eq 0$, and $x 
eq-y$.
Choose 1 answer:
(A) $\frac{x+y}{3}$
(B) $\frac{3}{x+y}$
(c) 3
(D) $\frac{1}{3}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To simplify the given expression $\frac{\frac{1}{y}+\frac{1}{x}}{\frac{3}{xy}}$, we first find a common denominator for $\frac{1}{y}$ and $\frac{1}{x}$, which is $xy$. ‖ ‖ step 2 ⋮ We rewrite the numerators over the common denominator: $\frac{x}{xy} + \frac{y}{xy}$. ‖ ‖ step 3 ⋮ Adding the fractions gives us $\frac{x+y}{xy}$. ‖ ‖ step 4 ⋮ Now we divide this by $\frac{3}{xy}$, which is the same as multiplying by its reciprocal, $\frac{xy}{3}$. ‖ ‖ step 5 ⋮ Multiplying $\frac{x+y}{xy}$ by $\frac{xy}{3}$ simplifies to $\frac{x+y}{3}$. ‖ ***A*** ∻Key Concept∻ ⚹Simplifying Complex Fractions⚹ ∻Explanation∻ ⚹To simplify a complex fraction, find a common denominator for the numerator's fractions, combine them, and then multiply by the reciprocal of the denominator's fraction.⚹◊What is the simplified form of the expression $\frac{\frac{1}{y}+\frac{1}{x}}{\frac{3}{xy}}$?⍭ Generate me a similar question◊

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