+0

# Simplifying complex Fractions

+1
122
7

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
+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
+2

x / (y sqrt3)     multiply by    sqrt3/sqrt3

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

Mar 29, 2022
#3
+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. $$\frac{\frac{x}{\sqrt3}}{y}\\ =\frac{x}{\sqrt3}\div y\\ =\frac{x}{\sqrt3}\times \frac{1}{y} \\ =\frac{x}{y\sqrt3}\qquad \text{I know that you already got this far} \\ \text{now you just need to reationalize the denominator}\\ =\frac{x}{y\sqrt3} \times \frac{\sqrt3}{\sqrt3}\\ =\frac{\sqrt3\; x}{3y}$$

Mar 30, 2022
#4
+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
+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
+1

Thank you all so much!

Elijah  Mar 30, 2022
#7
0

You are very welcome :)

Melody  Mar 30, 2022