Question

Write the expression as a single quotient (x+1)^(1/3) +(1/3)(x+1)^(-2/3)

My question is. What's to stop me from just doing this? (x+1)^(1/3) +(1/3)(x+1)^(-2/3)/1 and I am finished

Answer 1

First, you should also x^2 and x^3
Problem is the numerator will not be an integer value for integer x.
Can you try and fix that?

Answer 2

I editted my post, I posted another expression. Check it please.

Answer 3

No. Luis. It is not right.

Answer 4

No reason to bring the 3 up to numerator

Answer 5

Factor out (x+1)^(-2/3) from both terms. Then you can write it as one fraction.

Answer 6

\[(x+1)^{\frac{ 1 }{ 3 }}+\frac{ (x+1)^\frac{ -2 }{ 3 } }{ 3 }\]Make the denominators by same by multiplying the top and bottom of the first part by 3:\[ \frac{ 3(x+1)^{\frac{ 1 }{ 3 }} }{ 3} +\frac{ (x+1)^\frac{ -2 }{ 3 } }{ 3 }= \frac{3(x+1)^{\frac{ 1 }{ 3 }} +(x+1)^\frac{ -2 }{ 3 } }{ 3 }\]

Answer 7

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

Answer 8

@Mertsj what after that?

Answer 9

\[\frac{3(x+1)}{3(x+1)^{\frac{2}{3}}}+\frac{1}{3(x+1)^{\frac{2}{3}}}=\frac{3x+4}{3(x+1)^{\frac{2}{3}}}\]

Answer 10

so why I can't just so that to solve it? (x+1)^(1/3) +(1/3)(x+1)^(-2/3)/1

Answer 11

I just divided everything with 1

Answer 12

Dividing by 1 is not doing anything.

Answer 13

isn't it making it a quotient form?

Answer 14

No. It is trivial because anything divided by 1 is anything.

Answer 15

But wait. I have thought of something else.

Answer 16

Well.... then I can multiply evverything above by "2" and divide by 2 instead of 1? :))

Answer 17

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

Answer 18

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

Answer 19

ok. same result as before.