Question

Math

Posted 3 months ago

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

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Answer from Sia

Posted 3 months ago

Solution by Steps

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.

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