# Math Help - rationalise the denominator

1. ## rationalise the denominator

i am stuck rationalising the denominator of this -

(9√6 -8)/(√6 -1)

the book says (46 + √6) / 5

but i keep coming out with a numerator of 28 + √6 or something. if someone could step me through it the help would be much appreciated. thanks!

p.s my first ever time posting, i think this is the right section for this problem ^_^

2. Originally Posted by jacobc
i am stuck rationalising the denominator of this -

(9√6 -8)/(√6 -1)

the book says (46 + √6) / 5

but i keep coming out with a numerator of 28 + √6 or something. if someone could step me through it the help would be much appreciated. thanks!

p.s my first ever time posting, i think this is the right section for this problem ^_^

$\displaystyle \frac{9\sqrt{6}-8}{\sqrt{6}-1} \cdot \frac{\sqrt{6}+1}{\sqrt{6}+1} = \frac{54+\sqrt{6}-8}{6-1} = \frac{46+\sqrt{6}}{5}$

3. You're allowed to have a surd in the numerator and as you have the right denominator I assume it's an expansion error.

If you use FOIL on $(9\sqrt{6} - 8)(\sqrt{6}+1)$ and collect like terms you should get the book's answer

Spoiler:
$54+9\sqrt{6}-8\sqrt{6}-8$

4. thanks guys, i cant believe the mistake i made, i had 9*6 as 36 for some reason *Facepalm*