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Step-by-step explanation:
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Step-by-step explanation:
[tex] \frac{ \sqrt{1 + x} - \sqrt{1 - x} }{ \sqrt{1 + x} + \sqrt{1 - x} } [/tex]
=
[tex] \frac{ (\sqrt{1 + x} - \sqrt{1 - x} )( \sqrt{1 + x } - \sqrt{1 - x}) }{ (\sqrt{1 + x} + \sqrt{1 - x} )( \sqrt{1 + x} - \sqrt{1 - x} ) } [/tex]
=
[tex] \frac{{( \sqrt{1 + x} - \sqrt{1 - x} ) }^{2} }{ { \sqrt{1 + x} }^{2} - { \sqrt{1 - x} }^{2} } [/tex]
=
[tex] \frac{2 - 2 \sqrt{(1 + x)(1 - x)} }{2x} [/tex]
=
[tex] \frac{1 - \sqrt{(1 + x)(1 - x)} }{x} [/tex]