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\frac{1}{\sqrt{18+1}}
Add 9 and 9 to get 18.
\frac{1}{\sqrt{19}}
Add 18 and 1 to get 19.
\frac{\sqrt{19}}{\left(\sqrt{19}\right)^{2}}
Rationalize the denominator of \frac{1}{\sqrt{19}} by multiplying numerator and denominator by \sqrt{19}.
\frac{\sqrt{19}}{19}
The square of \sqrt{19} is 19.