Evaluate
\frac{5\left(\sqrt{19}-1\right)}{18}\approx 0.933027484
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\frac{4+1}{\sqrt{19}+1}
Calculate the square root of 16 and get 4.
\frac{5}{\sqrt{19}+1}
Add 4 and 1 to get 5.
\frac{5\left(\sqrt{19}-1\right)}{\left(\sqrt{19}+1\right)\left(\sqrt{19}-1\right)}
Rationalize the denominator of \frac{5}{\sqrt{19}+1} by multiplying numerator and denominator by \sqrt{19}-1.
\frac{5\left(\sqrt{19}-1\right)}{\left(\sqrt{19}\right)^{2}-1^{2}}
Consider \left(\sqrt{19}+1\right)\left(\sqrt{19}-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{5\left(\sqrt{19}-1\right)}{19-1}
Square \sqrt{19}. Square 1.
\frac{5\left(\sqrt{19}-1\right)}{18}
Subtract 1 from 19 to get 18.
\frac{5\sqrt{19}-5}{18}
Use the distributive property to multiply 5 by \sqrt{19}-1.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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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
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}