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# Prove That: (A+B+C)/(A^-1b^-1+B^-1c^-1+C^-1a^-1)=Abc - CBSE Class 9 - Mathematics

ConceptLaws of Exponents for Real Numbers

#### Question

Prove that:

(a+b+c)/(a^-1b^-1+b^-1c^-1+c^-1a^-1)=abc

#### Solution

Consider the left hand side:

(a+b+c)/(a^-1b^-1+b^-1c^-1+c^-1a^-1)

=(a+b+c)/(1/(ab)+1/(bc)+1/(ca))

=(a+b+c)/((c+a+b)/abc)

=(a+b+c)xx(abc/(a+b+c))

= abc

Therefore left hand side is equal to the right hand side. Hence proved.

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#### APPEARS IN

RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 2: Exponents of Real Numbers
Ex. 2.10 | Q: 5.1 | Page no. 12

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Solution Prove That: (A+B+C)/(A^-1b^-1+B^-1c^-1+C^-1a^-1)=Abc Concept: Laws of Exponents for Real Numbers.
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