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Which option gives the simplified form of (\frac{x^{-1}+y^{-1}}{(xy)^{-1}}), where (x\neq0) and (y\neq0)?
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Answer and explanation
Correct answer: (x+y)
Here (x^{-1}+y^{-1}=\frac{x+y}{xy}) and ((xy)^{-1}=\frac{1}{xy}), so division gives (x+y). In exams, converting negative exponents to fractions is safer.
Frequently asked questions
What is the correct answer to this question?
(x+y)
Why is this the correct answer?
Here (x^{-1}+y^{-1}=\frac{x+y}{xy}) and ((xy)^{-1}=\frac{1}{xy}), so division gives (x+y). In exams, converting negative exponents to fractions is safer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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