Math, asked by nancyroy28, 6 months ago

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Answered by rocky200216
6

\sf\underbrace{\red{CONCEPT:-}}

\checkmark\:\bf\underline{\purple{\boxed{{\dfrac{a^m}{a^n}}\:=\:a^{m-n}\:}}}

\sf\underbrace{\red{SOLUTION:-}}

 \frac{1}{1 +  {x}^{b - a} +  {x}^{c - a}  }  +  \frac{1}{1 +  {x}^{a - b} +  {x}^{c - b}  }  +  \frac{1}{1 +  {x}^{b - c} +  {x}^{a - c}  }  \\  \\  =  \frac{1}{1 +  \frac{ {x}^{b} }{ {x}^{a} } +  \frac{ {x}^{c} }{ {x}^{a} }  }  +  \frac{1}{1 +  \frac{ {x}^{a} }{ {x}^{b} } +  \frac{ {x}^{c} }{ {x}^{b} }  }  +  \frac{1}{1 +  \frac{ {x}^{b} }{ {x}^{c} } +  \frac{ {x}^{a} }{ {x}^{c} }  }  \\  \\  =  \frac{1}{ \frac{ {x}^{a} +  {x}^{b} +  {x}^{c}   }{ {x}^{a} } }  \frac{1}{ \frac{ {x}^{b} +  {x}^{a} +  {x}^{c}   }{ {x}^{b} } }  +  \frac{1}{ \frac{ {x}^{c} +  {x}^{b} +  {x}^{a}   }{ {x}^{c} } }  \\  \\  =  \frac{ {x}^{a} }{ {x}^{a} +  {x}^{b} +  {x}^{c}   }  +  \frac{ {x}^{b} }{ {x}^{b} +  {x}^{a} +  {x}^{c}   }  +  \frac{ {x}^{c} }{ {x}^{c} +  {x}^{b} +  {x}^{a}   }  \\  \\  =  \frac{ {x}^{a} +  {x}^{b} +  {x}^{c}   }{ {x}^{a} +  {x}^{b} +  {x}^{c}   }  \\  \\  = 1

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✔️ Hence, Solved

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Answered by ScienceMathsLover
1

Answer:

Here's your answer with explanation... Refer the attachment:

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