Question

Rationalize the denominator of 3/(4+sqrt5)+(3-2sqrt5)

Answer 1

it's not quite clear, do you mean, \[3/((4+\sqrt{5})+(3-2\sqrt{5}))\]

Answer 2

If you mean what EarthCitizen believes you do

Then the denominator can be simplified as \[1-\sqrt{5}\]
If you multiply by the complex conjugate
\[(1+\sqrt{5})(1-\sqrt5)\]
(1-5)
-4
You also have to multiply the numerator, so
\[3+3\sqrt{5}\]

Divide the whole thing by -4, and get
\[(3+3\sqrt{5})/-4\]

Answer 3

My options are
[3\sqrt{5}\-5+7sqrt{5}]
\[21+3\sqrt{5}/44\]
\[21+\sqrt{5}/44\]
\[21-3\sqrt{5}/54\]

Answer 4

Ah, that means I did something wrong. Let me check my work.

Answer 5

All right. It's the second option, 21+3√5 /44

When first simplifying the denominator, 4+3 is 7, meaning that all the ones should be sevens.

Answer 6

okay
thank you