Math, asked by manveersingh00910, 9 months ago

If a,b,c are integers, then
(A\b)/c not equal to a/(b/c) unless c=?

Answers

Answered by Swarup1998
4

If a,\:b,\:c are intergers, then \dfrac{\dfrac{a}{b}}{c}\neq \dfrac{a}{\dfrac{b}{c}} unless c=1.

Explanation:

  • The two fractions are:

  • \dfrac{\dfrac{a}{b}}{c}=\dfrac{a}{bc}

  • \dfrac{a}{\dfrac{b}{c}}=\dfrac{ac}{b}

  • Clearly, these fractions are not the same in general.

  • Let them be equal. Then,

  • \quad \dfrac{a}{bc}=\dfrac{ac}{b}

  • \Rightarrow \dfrac{1}{c}=c

  • \Rightarrow c^{2}=1

  • \Rightarrow \bold{c=1}

Thus we can conclude that c=1 is the only condition for the given fractions to be equal.

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