# Double Stacked Fraction

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• Apr 16th 2014, 11:29 PM
Katrena
Double Stacked Fraction
Okay, so here's my next drama:

Attachment 30691

It says the answer is: '√10a / 10'

However, how I am solving it is either multiplying either side by 2, then multiplying both sides again by the root 40 to rationalize the denominator.
The other way, dividing a/1 ÷ √40/2, then rationalizing, which gives me same wrong answer.
I've tried searching for ways to solve this type of question, but can't find anything. So please, how do I do this correctly?
• Apr 16th 2014, 11:39 PM
romsek
Re: Double Stacked Fraction
in general

$\dfrac 1 {\dfrac a b}=\dfrac b a$

applied here we get

$\dfrac a {\dfrac{\sqrt{40}} 2}=a \cdot \dfrac 2 {\sqrt{40}}=\dfrac{2a}{\sqrt{4\cdot 10}}=\dfrac{2a}{2\sqrt{10}} =\dfrac a {\sqrt{10}}=\dfrac a {\sqrt{10}}\dfrac{\sqrt{10}}{\sqrt{10}}=\dfrac {\sqrt{10}a}{10}$
• Apr 17th 2014, 12:00 AM
Katrena
Re: Double Stacked Fraction
Ohh, ffs. I forgot about simplifying the root. That's where I went wrong. Thanks