Evaluate
\frac{\sqrt{7}}{7}+\frac{1}{3}\approx 0.711297806
Factor
\frac{\sqrt{7} {(\sqrt{7} + 3)}}{21} = 0.7112978063425606
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\frac{1}{\sqrt{7}}+\frac{1}{3}
Add 5 and 2 to get 7.
\frac{\sqrt{7}}{\left(\sqrt{7}\right)^{2}}+\frac{1}{3}
Rationalize the denominator of \frac{1}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.
\frac{\sqrt{7}}{7}+\frac{1}{3}
The square of \sqrt{7} is 7.
\frac{3\sqrt{7}}{21}+\frac{7}{21}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and 3 is 21. Multiply \frac{\sqrt{7}}{7} times \frac{3}{3}. Multiply \frac{1}{3} times \frac{7}{7}.
\frac{3\sqrt{7}+7}{21}
Since \frac{3\sqrt{7}}{21} and \frac{7}{21} have the same denominator, add them by adding their numerators.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
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}