Đáp án:
\(\begin{array}{l}
a) - 2\sqrt 3 - 5\\
b) - 2\sqrt 5 - 6\\
c)\dfrac{{5\sqrt 2 + 2\sqrt 5 }}{{30}}\\
d) - 6 + \sqrt {35}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\dfrac{{13}}{{2\sqrt 3 - 5}} = \dfrac{{13\left( {2\sqrt 3 + 5} \right)}}{{4.3 - 25}}\\
= - \dfrac{{13\left( {2\sqrt 3 + 5} \right)}}{{13}}\\
= - \left( {2\sqrt 3 + 5} \right)\\
= - 2\sqrt 3 - 5\\
b)\dfrac{8}{{\sqrt 5 - 3}} = \dfrac{{8\left( {\sqrt 5 + 3} \right)}}{{5 - 9}}\\
= - \dfrac{{8\left( {\sqrt 5 + 3} \right)}}{4}\\
= - 2\left( {\sqrt 5 + 3} \right)\\
= - 2\sqrt 5 - 6\\
c)\dfrac{1}{{5\sqrt 2 - 2\sqrt 5 }} = \dfrac{{5\sqrt 2 + 2\sqrt 5 }}{{25.2 - 4.5}}\\
= \dfrac{{5\sqrt 2 + 2\sqrt 5 }}{{30}}\\
d)\dfrac{{\sqrt 5 - \sqrt 7 }}{{\sqrt 5 + \sqrt 7 }} = \dfrac{{{{\left( {\sqrt 5 - \sqrt 7 } \right)}^2}}}{{5 - 7}}\\
= - \dfrac{{5 - 2\sqrt {35} + 7}}{2}\\
= - \dfrac{{12 - 2\sqrt {35} }}{2}\\
= - 6 + \sqrt {35}
\end{array}\)
