Simplify
[tex]\[\frac{{{c^{\frac{1}{2}}} - {d^{\frac{1}{2}}}}}{{{c^{\frac{1}{2}}} + {d^{\frac{1}{2}}}}}\][/tex]
Solution:
[tex]\[\begin{array}{l}\frac{{{c^{\frac{1}{2}}} - {d^{\frac{1}{2}}}}}{{{c^{\frac{1}{2}}} + {d^{\frac{1}{2}}}}}\\\\ = \frac{{\sqrt c - \sqrt d }}{{\sqrt c + \sqrt d }}\\\\ = \frac{{\sqrt c - \sqrt d }}{{\sqrt c + \sqrt d }} \bullet \frac{{\sqrt c - \sqrt d }}{{\sqrt c - \sqrt d }}\\\\ = \frac{{{{(\sqrt c - \sqrt d )}^2}}}{{c + \sqrt c \sqrt d - \sqrt c \sqrt d - d}}\\\\ = \frac{{{{(\sqrt c - \sqrt d )}^2}}}{{c - d}}\end{array}\][/tex]
Answer:
[tex]\[ = \frac{{{{(\sqrt c - \sqrt d )}^2}}}{{c - d}}\][/tex]
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