Question

$\frac{1}{ {x}^{a - b} + 1} + \frac{1}{ {x}^{b - a} + 1}$
​Please answer this question I will make you as brainlist

Answer 1

✰Answer✰

❋Before solving, Let discuss some important concepts of indices or exponents.

♦️Here are some important laws:

$\large{ \sf{ \star{ \: {a}^{m} \times {a}^{n} = {a}^{m + n} }}} \\ \\ \large{ \sf{ \star{ \: {a}^{m} \div {a}^{n} = {a}^{m - n} }}} \\ \\ \large{ \sf{ \star{ \: ({a}^{m} ) {}^{n} = {a}^{mn} }}} \\ \\ \large{ \sf{ \star{ \: {a}^{1} = a}}} \\ \\ \large{ \sf{ \star{ \: {a}^{0} = 1}}} \\ \\ \large{ \sf{ \star{ \: ( { \frac{a}{b} })^{m} = \frac{ {a}^{m} }{ {b}^{m} } }}} \\ \\ \large{ \sf{ \star{ \: {a}^{ - m} = \frac{1}{ {a}^{m} } }}} \\ \\ \large{ \sf{ \star{ \: {a}^{ \frac{x}{y} } = \sqrt[y]{ {a}^{x} } }}}$

☛By using these laws, we will find

✰Solution✰

$\large{ \sf{ \rightarrow \: \frac{1}{1 + {x}^{a - b} } \: + \: \frac{1}{1 + {x}^{b - a} } }} \\ \\ \large{ \sf{ \rightarrow \: \frac{1}{1 + \frac{ {x}^{a} }{ {x}^{b} } } \: + \: \frac{1}{1 + \frac{ {x}^{b} }{ {x}^{a} } } }} \\ \\ \large{ \sf{ \rightarrow \: \frac{1}{ \frac{ {x}^{b} + {x}^{a} }{ {x}^{b} }} + \frac{1}{ \frac{x {}^{a} + {x}^{b} }{ {x}^{a} } } }} \\ \\ \large{ \sf{ \rightarrow \: \frac{ {x}^{b} }{ {x}^{a} + {x}^{b} } \: + \: \frac{ {x}^{a} }{ {x}^{a} + {x}^{b} } }} \\ \\ \large{ \sf{ \rightarrow \: \cancel{ \frac{ {x}^{a} + {x}^{b} }{ {x}^{a} + {x}^{b} } }}} \\ \\ \large{ \sf{ \boxed{ \rightarrow \: \boxed{ \purple{1}}}}}$

✰So Final Answer✰

$\large{ \boxed{ \bf{ = 1}}}$