Question

please solve my question correctly and don't spam..... explanation must...​

Answer 1

Solution:-To prove:-

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

Proof:-Take LHS

$\frac{1}{1 + \frac{ {x}^{b} }{ {x}^{a} } + \frac{ {x}^{c} }{ {x}^{a} } } + \frac{1}{1 + \frac{ {x}^{a} }{ {x}^{b} } + \frac{ {x}^{c} }{ {x}^{b} } } + \frac{1}{1 + \frac{ {x}^{a} }{ {x}^{c} } + \frac{ {x}^{b} }{ {x}^{c} } } \\ take \: {x}^{a} \: lcm \:from \: first \: term \: \: \: \: {x}^{b} in \: second \: term \: \: and \: {x}^{c} \: im \: \\ third \: term \\ \frac{1}{ \frac{ {x}^{a} + {x}^{b} + {x}^{c} }{ {x}^{a} } } + \frac{1}{ \frac{ {x}^{b} + {x}^{a} + {x}^{c} }{ {x}^{b} } } + \frac{1}{ \frac{ {x}^{c} + {x}^{a} + {x}^{b} }{ {x}^{c} } } \\ \frac{ {x}^{a} }{ {x}^{a} + {x}^{b} + {x}^{c} + } + \frac{ {x}^{b} }{ {x}^{a} + {x}^{b} + {x}^{c} } + \frac{ {x}^{c} }{ {x}^{a} + {x}^{b} + {x}^{c} } \\ taking \: {x}^{a} + {x}^{b} + {x}^{c} \: as \: lcm \: we \: get \\ \frac{ {x}^{a} + {x}^{b} + {x}^{c} }{ {x}^{a} + {x}^{b} + {x}^{c} } = 1$

this is equal to RHS

Hence proved

{hope it helps you}