anonymous one year ago Rationalize the numerator: sqrt(m) + sqrt(m^2 - 5) -------------------- sqrt(m) - sqrt(m^2 - 5) I keep getting stuck when trying to simplify.

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1. dinamix

sqrt(m) + sqrt(m^2 - 5) sqrt(m) + sqrt(m^2 - 5) m + m^2-5 +2sqrt(m^3-5m) -------------------- x ---------------------- =------------------------- sqrt(m) - sqrt(m^2 - 5) sqrt(m) + sqrt(m^2 - 5) m-m^2+5

2. dinamix

$=\frac{ m+m^2-5+2{m^3-5m} }{ m-m^2+5}$

3. dinamix

@javaj0hn

4. freckles

$(\sqrt{m}+\sqrt{m^2-5})(\sqrt{m}+\sqrt{m^2-5}) \\m+2 \sqrt{m} \sqrt{m^2-5}+(m^2-5) \neq m+m^2-5$ but also he wanted to rationalize numerator so we should multiply top and bottom by $\sqrt{m}-\sqrt{m^2-5}$

5. freckles

oh you got m+m^2-5+2sqrt(m^3-5m) and then you went to m+m^2-5+2m^3-5m so I think it was just a type-o maybe but this will still lead to the numerator not being rationalized