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\frac{\left(\sqrt{2}-1\right)\left(\sqrt{2}-1\right)}{\left(\sqrt{2}\right)^{2}-1^{2}}
Consider \left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{\left(\sqrt{2}-1\right)\left(\sqrt{2}-1\right)}{2-1}
Square \sqrt{2}. Square 1.
\frac{\left(\sqrt{2}-1\right)\left(\sqrt{2}-1\right)}{1}
Subtract 1 from 2 to get 1.
\left(\sqrt{2}-1\right)\left(\sqrt{2}-1\right)
Anything divided by one gives itself.
\left(\sqrt{2}-1\right)^{2}
Multiply \sqrt{2}-1 and \sqrt{2}-1 to get \left(\sqrt{2}-1\right)^{2}.
\left(\sqrt{2}\right)^{2}-2\sqrt{2}+1
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{2}-1\right)^{2}.
2-2\sqrt{2}+1
The square of \sqrt{2} is 2.
3-2\sqrt{2}
Add 2 and 1 to get 3.