Question

pls answer it faster​

Answer 1

ANSWER

yes it is true

it is an identity true for all values of x

proof is in attachment

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Answer 2

Step-by-step explanation:

Questions

To prove

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

Formula

$\frac{1}{ {a}^{ - 1} } = a$

Solutions

prove

LHS

$\frac{1}{1 + {x}^{a - b} } + \frac{1}{1 + {x}^{b - a} } \\ taking \: common \: - 1 \: in \: b \: - a \: we \: get \\ \frac{1}{ {x}^{a - b} } + \frac{1}{1 + \frac{1}{ {x}^{a - b} } } \\ \frac{1}{ {x}^{a - b} } + \frac{ {x}^{a - b} }{ {x}^{a - b} + 1}$

Now

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

1

Hence LHS = RHS

proved