Question

Quiz by 匚ㄖ爪卩ㄥ乇乂乂
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[tex] \frac{ \sqrt{7} - \sqrt{8} }{ \sqrt{5} + \sqrt{3} } = \\ [/tex]
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Answer 1

Verified answer

[tex] \frac{ \sqrt{7} - \sqrt{8} }{ \sqrt{5} + \sqrt{3} } [/tex]

[tex] = \frac{ \sqrt{7} - \sqrt{8} }{ \sqrt{5} + \sqrt{3} } \times \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} - \sqrt{3} } [/tex]

[tex] = \frac{ (\sqrt{7} \times \sqrt{5}) - ( \sqrt{3} \times \sqrt{7} ) - ( \sqrt{8} \times \sqrt{5}) + ( \sqrt{8} \times \sqrt{3} )}{5 - 3} [/tex]

[tex] = \frac{ \sqrt{35} - \sqrt{21} - \sqrt{40} + \sqrt{24} }{2} [/tex]

[tex] = \frac{ \sqrt{35} - \sqrt{21} - (\sqrt{4 \times 10} )+ (\sqrt{4 \times 6} ) }{2} [/tex]

[tex] = \frac{ \sqrt{35} - \sqrt{21} - 2 \sqrt{10} + 2 \sqrt{6} }{2} [/tex]