Question

Rationalize the numerator:

sqrt(m) + sqrt(m^2 - 5)
--------------------
sqrt(m) - sqrt(m^2 - 5)

I keep getting stuck when trying to simplify.

Answer 1

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

Answer 2

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

Answer 3

@javaj0hn

Answer 4

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

Answer 5

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