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avatar+488 

I Am Supposed to be simplifying this\(\frac{\frac{x}{\sqrt{3}}}{y}\)

Ive gotten as far as bringing the Y up to make it \(\frac{x}{\sqrt{3}y}\)

What is the next step?

THanks in advance

 Mar 29, 2022
 #1
avatar+2437 
+1

Multiply both the numerator and the denominator by \(y \over \sqrt3\), the reciprocal of \(\sqrt3 \over y\)

 

This gives: \(xy\over \sqrt3\), which can be written as \(xy \sqrt3 \over 3\)

 Mar 29, 2022
 #2
avatar+36433 
+2

x / (y sqrt3)     multiply by    sqrt3/sqrt3

 

x sqrt 3 /  3y        or     x y-1  sqrt 3 / 3

 Mar 29, 2022
 #3
avatar+117821 
+1

Thanks Bilderboi and EP

You did make a mistake builder boi which EP picked up on. 

Here is my answer just to stop any confusion.  laugh

 

\(\frac{\frac{x}{\sqrt3}}{y}\\ =\frac{x}{\sqrt3}\div y\\ =\frac{x}{\sqrt3}\times \frac{1}{y} \\ =\frac{x}{y\sqrt3}\qquad \text{I know that you already got this far} \\ \text{now you just need to reationalize the denominator}\\ =\frac{x}{y\sqrt3} \times \frac{\sqrt3}{\sqrt3}\\ =\frac{\sqrt3\; x}{3y} \)

 Mar 30, 2022
 #4
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+2

2nd line is that a sqrt of 3? or a sqrt of 3y? Not to judge, but I think it's more formal to write it as y sqrt of 3

 Mar 30, 2022
 #5
avatar+117821 
+2

It is written  as (square root of 3) times y    ---  which is correct.

 

\(\sqrt3y \qquad not\quad \sqrt{3y}\)

Melody  Mar 30, 2022
 #6
avatar+488 
+1

Thank you all so much! 

Elijah  Mar 30, 2022
 #7
avatar+117821 
0

You are very welcome :)

Melody  Mar 30, 2022

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