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# Simplifying complex Fractions

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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?

Mar 29, 2022

#1
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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
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x / (y sqrt3)     multiply by    sqrt3/sqrt3

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

Mar 29, 2022
#3
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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.

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

Mar 30, 2022
#4
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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
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It is written  as (square root of 3) times y    ---  which is correct.

$$\sqrt3y \qquad not\quad \sqrt{3y}$$

Melody  Mar 30, 2022
#6
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Thank you all so much!

Elijah  Mar 30, 2022
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You are very welcome :)

Melody  Mar 30, 2022