Question

please help me out ​

Answer 1

Required Answer

Solution :

$\tt \: \frac{1}{1 + {x}^{b - a} + {x}^{c - a} } + \frac{1}{1 + {x}^{a - b} + {x}^{c - b} } + \frac{1}{1 + {x}^{b - c} {x}^{a - c} } \\ \\ \\ \\ : \implies \: \tt \: \frac{ {x}^{a} }{ {x}^{a} \bigg(1 + {x}^{b - a} + {x}^{c - a} \bigg) } + \frac{ {x}^{b} }{ {x}^{b} \bigg(1 + {x}^{a - b} + {x}^{c - b} \bigg)} + \frac{ {x}^{c} }{ {x}^{c} \bigg( 1 + {x}^{b - c} + {x}^{a - c} \bigg) } \\ \\ \\ \\ : \implies \tt \frac{ {x}^{a} }{ {x}^{a} + {x}^{b} + {x}^{c} } + \frac{ {x}^{b} }{ {x}^{b} + {x}^{a} + {x}^{c} } + \frac{ {x}^{c} }{ {x}^{c} + {x}^{b} + {x}^{a} } \\ \\ \\ \\ : \implies \tt \bigg(\frac{ \cancel{{x}^{a} + {x}^{b} + {x}^{c}} }{ \cancel{ {x}^{a} + {x}^{b} + {x}^{c} } } \bigg) \\ \\ \\ \\ \bf \: \large : \implies \large \: { \bf \: 1} \\ \\ \\ \\ \huge \red{ \mathfrak{Happy \: \: New \: \: Year \: \: 2021}} \\ \\ \\ \\ \small \tt \colorbox{aqua}{@StayHigh}$

Answer 2

$\sf{\bold{\blue{\underline{\underline{Given}}}}}$

$\begin{gathered} \tt \: \frac{1}{1 + {x}^{b - a} + {x}^{c - a} } + \frac{1}{1 + {x}^{a - b} + {x}^{c - b} } + \frac{1}{1 + {x}^{b - c} {x}^{a - c} }\end{gathered}$⠀⠀⠀

$\sf{\bold{\red{\underline{\underline{To\:Find}}}}}$

●Simplified this equation. ⠀⠀⠀⠀

$\sf{\bold{\purple{\underline{\underline{Solution}}}}}$

⠀⠀⠀⠀

$\begin{gathered} \tt \: \frac{1}{1 + {x}^{b - a} + {x}^{c - a} } + \frac{1}{1 + {x}^{a - b} + {x}^{c - b} } + \frac{1}{1 + {x}^{b - c} {x}^{a - c} } \\ \\ \\ \\ \rightsquigarrow \: \tt \: \frac{ {x}^{a} }{ {x}^{a} \bigg(1 + {x}^{b - a} + {x}^{c - a} \bigg) } + \frac{ {x}^{b} }{ {x}^{b} \bigg(1 + {x}^{a - b} + {x}^{c - b} \bigg)} + \frac{ {x}^{c} }{ {x}^{c} \bigg( 1 + {x}^{b - c} + {x}^{a - c} \bigg) } \\ \\ \\ \\ \rightsquigarrow \tt \frac{ {x}^{a} }{ {x}^{a} + {x}^{b} + {x}^{c} } + \frac{ {x}^{b} }{ {x}^{b} + {x}^{a} + {x}^{c} } + \frac{ {x}^{c} }{ {x}^{c} + {x}^{b} + {x}^{a} } \\ \\ \\ \\ \rightsquigarrow\tt \bigg(\frac{ \cancel{{x}^{a} + {x}^{b} + {x}^{c}} }{ \cancel{ {x}^{a} + {x}^{b} + {x}^{c} } } \bigg) \\ \\ \\ \\ \bf \: \large \rightsquigarrow \large \: {\tt 1 }\end{gathered}$