Question

simplify
$simplify \frac{ \sqrt{2} - 1 }{ \sqrt{2} + 1 }$

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{ \sqrt{2} - 1 }{ \sqrt{2} + 1} \\ \\ on \: rationalizing \: we \: get \\ \\ = \frac{ \sqrt{2} - 1}{ \sqrt{2} + 1 } \times \frac{ \sqrt{2} - 1}{ \sqrt{2} - 1} \\ \\ using \: the \: identities \\ {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{ {( \sqrt{2} )}^{2} + {(1)}^{2} - 2 \times \sqrt{2} \times 1}{ {( \sqrt{2}) }^{2} - {(1)}^{2} } \\ \\ = \frac{2 + 1 - 2 \sqrt{2} }{2 - 1} \\ \\ = 3 - 2 \sqrt{2}$

Hope this helps!!!!

@Mahak24

Thanks....
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