Evaluate
\sqrt{2}-1\approx 0.414213562
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\frac{\sqrt{2}-1}{\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)}
Rationalize the denominator of \frac{1}{\sqrt{2}+1} by multiplying numerator and denominator by \sqrt{2}-1.
\frac{\sqrt{2}-1}{\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{\sqrt{2}-1}{2-1}
Square \sqrt{2}. Square 1.
\frac{\sqrt{2}-1}{1}
Subtract 1 from 2 to get 1.
\sqrt{2}-1
Anything divided by one gives itself.
Examples
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y = 3x + 4
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Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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