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Question
Math
Posted 3 months ago
Which expression is equivalent to 1y+1x3xy\frac{\frac{1}{y}+\frac{1}{x}}{\frac{3}{x y}} ?
Assume x0,y0x \neq 0, y \neq 0, and xyx \neq-y.
Choose 1 answer:
(A) x+y3\frac{x+y}{3}
(B) 3x+y\frac{3}{x+y}
(c) 3
(D) 13\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: xxy+yxy\frac{x}{xy} + \frac{y}{xy}
step 3
Adding the fractions gives us x+yxy\frac{x+y}{xy}
step 4
Now we divide this by 3xy\frac{3}{xy}, which is the same as multiplying by its reciprocal, xy3\frac{xy}{3}
step 5
Multiplying x+yxy\frac{x+y}{xy} by xy3\frac{xy}{3} simplifies to x+y3\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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