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anonymous
 one year ago
How would I find the least common denominator of these fractions (posted below)...
anonymous
 one year ago
How would I find the least common denominator of these fractions (posted below)...

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ \sqrt[3]{x} }{ 2\sqrt{x} } + \frac{ \sqrt{x}+3 }{ 3\sqrt[3]{x} }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lol That's exactly what I thought.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0at first i thought you be like 1/18 and 1/4 or something like that and I be like I know EXACTLY how to do that :) but ya... no...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0See that's my problem, and I even know the answer (thanks to calculators). Problem is I have to show work, and I can't do that since I have no idea how to. But yeah. Don't worry about it. :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Ashleyisakitty @west_coast

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It would be appreciated. :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok, paste both fractions in separate comments so i can see them clearer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1442863551641:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay just a second. (and nice picture lol)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ \sqrt[3]{x} }{ 2\sqrt{x} }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ehhhhhhhh................. idk thiss

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ \sqrt{x}+3 }{ 3\sqrt[3]{x} }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Nnesha @Preetha @kiamousekia @iGreen

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would you like help with this \[\frac{ \sqrt[3]{x} }{ 2\sqrt{x} } + \frac{ \sqrt{x}+3 }{ 3\sqrt[3]{x} }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0$$\Large \frac{ \sqrt[3]{x} }{ 2\sqrt{x} }\cdot \frac{\sqrt x }{\sqrt x } + \frac{ \sqrt{x}+3 }{ 3\sqrt[3]{x} } \cdot \frac{\sqrt[3] {x^2} }{\sqrt[3] {x^2}} $$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0First i would rationalize the denominators

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is what you posted above the rationalization?

phi
 one year ago
Best ResponseYou've already chosen the best response.2it might be easier to see if you know how to write the radicals as exponents \[ \frac{ \sqrt[3]{x} }{ 2\sqrt{x} } + \frac{ \sqrt{x}+3 }{ 3\sqrt[3]{x} } \\ \frac{ x^\frac{1}{3} }{ 2x^\frac{1}{2} } + \frac{ x^\frac{1}{2} +3 }{ 3x^\frac{1}{3} } \] the common denominator is the product of the two denominators you can also rationalize the denominators as jayz suggests. notice that the answer can be written in many different forms

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So \[6x^{1/6}\] would be the common denominator ?

phi
 one year ago
Best ResponseYou've already chosen the best response.2you add exponents so 6 x^(5/6) you can remember this rule by remembering x *x = x^2 and x is x^1 in other words, \( x^1 \cdot x^1 = x^2\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ah okay. Just to check, is this a problem that I have to multiply the numerators by the same values as the denominators?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Because I have heard both yes and no from different people depending on the equations.

phi
 one year ago
Best ResponseYou've already chosen the best response.2once you know what the common denominator is, you know what you should multiply the "bottom" by (in the the first fraction, for example) we can't just multiply the bottom by something (that will change it) but if we multiply top and bottom by the same thing (for example x/x) that is the same as multiplying by 1 , so it does not change the fraction.

phi
 one year ago
Best ResponseYou've already chosen the best response.2\[ \frac{ x^\frac{1}{3} }{ 2x^\frac{1}{2} } + \frac{ x^\frac{1}{2} +3 }{ 3x^\frac{1}{3} } \] multiply the first fraction by 1 (in the form 3 x^(1/3) / (3 x^(1/3)) \[ \frac{ x^\frac{1}{3} }{ 2x^\frac{1}{2} } \cdot \frac{ 3x^\frac{1}{3} }{ 3x^\frac{1}{3} }+ \frac{ x^\frac{1}{2} +3 }{ 3x^\frac{1}{3} } \]

phi
 one year ago
Best ResponseYou've already chosen the best response.2and multiply the second fraction by 1 in the form 2x^(1/2) / 2x^(1/2) \[ \frac{ x^\frac{1}{3} }{ 2x^\frac{1}{2} } \cdot \frac{ 3x^\frac{1}{3} }{ 3x^\frac{1}{3} }+ \frac{ (x^\frac{1}{2} +3 )}{ 3x^\frac{1}{3} }\cdot \frac{ 2x^\frac{1}{2} }{ 2x^\frac{1}{2} }\]

phi
 one year ago
Best ResponseYou've already chosen the best response.2I assume you know how to add the exponents 1/2 + 1/3 that is the same as 3/6 + 2/6 = 5/6

phi
 one year ago
Best ResponseYou've already chosen the best response.2so you get 6 x^(5/6) as the common denominator

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, I understand. Thank you. :) I am solving it out now.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got\[\frac{ 3x^{2/3}+2\sqrt{x} (\sqrt{x}+3) }{ 6x^{5/6} }\]

phi
 one year ago
Best ResponseYou've already chosen the best response.2yes, and that can be written as \[ \frac{ 3x^\frac{2}{3} + 2x + 6 x^\frac{1}{2}}{6x^\frac{5}{6}} \] and lots of other ways. for example: \[ \frac{1}{2x^\frac{1}{6}} + \frac{x^\frac{1}{6}}{3} +\frac{1}{x^\frac{1}{3}} \] (all ways look ugly!)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And that would be the final answer correct?

phi
 one year ago
Best ResponseYou've already chosen the best response.2I think as good as any is \[ \frac{ 3x^\frac{2}{3} + 2x + 6 x^\frac{1}{2}}{6x^\frac{5}{6}} \] (that is your answer, but "distributing" the \( 2 \sqrt{x}\) on the other hand some people would rather have the denominator 6x (rather than 6 x^(5/6) ) so they would multiply top and bottom by x^(1/6)) But I would leave it the first way. Or show your teacher the different ways and ask if it matters.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The way you did it makes sense to me, so I'm going with that one. Thank you so much for your help! :D
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