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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If (x+1)^{1/3}-{1}{3}x(x+1)^{-2/3}}{(x+1)^{2/3}}=0 then x =

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Intern  B
Joined: 04 Jan 2017
Posts: 14
If (x+1)^{1/3}-{1}{3}x(x+1)^{-2/3}}{(x+1)^{2/3}}=0 then x =  [#permalink]

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2
6 00:00

Difficulty:   65% (hard)

Question Stats: 61% (02:11) correct 39% (02:51) wrong based on 241 sessions

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If $$\frac{(x+1)^{1/3}-\frac{1}{3}x(x+1)^{-2/3}}{(x+1)^{2/3}}=0$$ , then x =

A. -3/2
B. -2/3
C. 0
D. 1/3
E. 1

Source: NOVA Math Review
Intern  B
Joined: 04 Jan 2017
Posts: 14
Re: If (x+1)^{1/3}-{1}{3}x(x+1)^{-2/3}}{(x+1)^{2/3}}=0 then x =  [#permalink]

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I am a bit lost on this one. I keep getting -2/3 for an answer but OA is -3/2... My algebra skills are a bit rusty so I would be happy to see a step by step explanation of how to attack this beast...
Manager  D
Joined: 12 Mar 2013
Posts: 233
Re: If (x+1)^{1/3}-{1}{3}x(x+1)^{-2/3}}{(x+1)^{2/3}}=0 then x =  [#permalink]

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3
1
denominator can't be zero. So (x+1)^1/3−1/3*x*(x+1)^−2/3 =0
(x+1)^1/3=1/3*x*(x+1)^−2/3
(x+1)^1/3= 1/3*x * 1/(x+1)^2/3
x+1= 1/3*x
3x+3=x
x=-3/2
A
_________________
We Shall Overcome... One day...
Intern  B
Joined: 04 Jan 2017
Posts: 14
Re: If (x+1)^{1/3}-{1}{3}x(x+1)^{-2/3}}{(x+1)^{2/3}}=0 then x =  [#permalink]

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Thanks! I failed to realize that we can simply multiply away the denominator and got lost in my attempts to factor the expression out. That makes the whole expression much less daunting...
Manager  D
Joined: 12 Mar 2013
Posts: 233
Re: If (x+1)^{1/3}-{1}{3}x(x+1)^{-2/3}}{(x+1)^{2/3}}=0 then x =  [#permalink]

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You are welcome brother.
_________________
We Shall Overcome... One day...
Director  S
Joined: 12 Nov 2016
Posts: 700
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37 GRE 1: Q157 V158 GPA: 2.66
Re: If (x+1)^{1/3}-{1}{3}x(x+1)^{-2/3}}{(x+1)^{2/3}}=0 then x =  [#permalink]

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1
denominator can't be zero. So (x+1)^1/3−1/3*x*(x+1)^−2/3 =0
(x+1)^1/3=1/3*x*(x+1)^−2/3
(x+1)^1/3= 1/3*x * 1/(x+1)^2/3
x+1= 1/3*x
3x+3=x
x=-3/2
A

I don't understand how you canceled out the 1/(x +1)^2/3
Math Expert V
Joined: 02 Aug 2009
Posts: 7967
Re: If (x+1)^{1/3}-{1}{3}x(x+1)^{-2/3}}{(x+1)^{2/3}}=0 then x =  [#permalink]

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Scyzo wrote:
If $$\frac{(x+1)^{1/3}-\frac{1}{3}x(x+1)^{-2/3}}{(x+1)^{2/3}}=0$$ , then x =

A. -3/2
B. -2/3
C. 0
D. 1/3
E. 1

Source: NOVA Math Review

Hi,

Denominator cannot be ZERO, otherwise the fraction will not be 0 but undefined..

So $$(x+1)^{1/3}-\frac{1}{3}x(x+1)^{-2/3}=0$$
Since exponent of (x+1) is -2/3, take it in denominator and change the sign..
OR multiply both sides by (x+1)^2/3.....
$$(x+1)^{1/3}*(x+1)^{2/3}-\frac{1}{3}x(x+1)^{-2/3}*(x+1)^{2/3}=0$$.....
$$(x+1)^{1/3+2/3}-\frac{1}{3}x(x+1)^{-2/3+2/3}=0$$..
$$(x+1)-\frac{1}{3}x=0$$....
$$x+1-\frac{x}{3}=0......\frac{2x}{3}=-1..... x=-1*\frac{3}{2}=\frac{-3}{2}$$
A
_________________
Intern  Joined: 31 Jan 2017
Posts: 1
Re: If (x+1)^{1/3}-{1}{3}x(x+1)^{-2/3}}{(x+1)^{2/3}}=0 then x =  [#permalink]

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How do you know when you can multiply the denominator by 0 (i.e. eliminate the denominator) and when you can't? If you have a fraction = zero, can you always just multiply the denominator by 0?
Intern  B
Joined: 07 Dec 2016
Posts: 6
Re: If (x+1)^{1/3}-{1}{3}x(x+1)^{-2/3}}{(x+1)^{2/3}}=0 then x =  [#permalink]

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Scyzo wrote:
If $$\frac{(x+1)^{1/3}-\frac{1}{3}x(x+1)^{-2/3}}{(x+1)^{2/3}}=0$$ , then x =

A. -3/2
B. -2/3
C. 0
D. 1/3
E. 1

Source: NOVA Math Review

The hardest part is to imagine the 1/3 part. So better assign a value to it, let (x+1)^1/3 = a
Then the eqn eventually becomes

3a^3 -x = 0
now from here its easy to find the solution. 50 seconds to solve this qn!!! kudos
The trick lies in the imagination!!!
Intern  B
Joined: 16 May 2018
Posts: 2
Re: If (x+1)^{1/3}-{1}{3}x(x+1)^{-2/3}}{(x+1)^{2/3}}=0 then x =  [#permalink]

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Take $$(x+1)^-2/3$$ common in the numerator:

Eqn then becomes :

$$(x+1)^-\frac{2}{3}$$[ (x+1) - x/3]/$$(x+1)^\frac{2}{3}$$

Cancelling $$(x+1)^\frac{-2}{3}$$, we have :

x+1-$$\frac{x}{3}$$ = 0
= 2x = -3
or x= $$\frac{-3}{2}$$ Re: If (x+1)^{1/3}-{1}{3}x(x+1)^{-2/3}}{(x+1)^{2/3}}=0 then x =   [#permalink] 24 Jul 2018, 04:52
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