Question

prove: 1/1+x raise to power a-b +1/1+x raise to power b-a

Answer 1

$\frac{1}{(1 + x) {}^{(a - b)} } + \frac{1}{(1 + x) {}^{(b -a) } } {}$
$\frac{1}{ {(1 + x)}^{a} \div {(1 + x)}^{b} } + \frac{1}{ {(1 + x)}^{b} \div {(1 + x)}^{a} }$
$\frac{ {(1 + x)}^{b} }{ {(1 + x)}^{a} } + \frac{ {(1 + x)}^{a} }{ {(1 + x)}^{b} }$
$\frac{ {(1 + x)}^{2b} + {(1 + x)}^{2a} }{ {(1 + x)}^{a + b} }$
$\frac{ {(1 + x)}^{2a + 2b} }{ {(1 + x)}^{a + b} }$
$\frac{ {(1 + x)}^{ {(a + b)}{2} } }{ {(1 + x)}^{a + b} }$
${1}^{2}$
=1


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