Algebraic simplifications pro level

[gh0st]

http://www.math.ucdavis.edu/~marx/algsimpPr1/algsimpPr1.html

Pr1 I cannot do it I get a different solution

Here are the solutions watch sol1

http://www.math.ucdavis.edu/~marx/algsimpSol/algsimpSol.html

Plz help

[gh0st]

guys plz help :3 it seems easy but if you dont get the answer as it says in the solutions it proves that you are doing it wrong i cant get something close to it

[Mordred]

I hope I got the correct exercise.

5/3[x^(2/3)] - 10/3[x^(-1/3)]

so the powers are only for the x, not for the 3 as well

5/3[x^(2/3)] - 10/3[x^(-1/3)] = 5/3x^(-1/3) * (x-2)

You take the factor 5/3x^(-1/3) out in front of the parentheses. Then what you want to calculate is the following:

1. {5/3[x^(2/3)]} / {5/3[x^(-1/3)]} = x - I hope this is obvious considering the fact that the terms are identical with the exception of the power of x. Considering one is 2/3 and the other is -1/3 and you will subtract them, the power of x will be 2/3-(-1/3) = 2/3 + 1/3 = 1
2. {10/3[x^(-1/3)]} / {5/3[x^(-1/3)]} = 2 - this should also be obvious because the powers are identical, the only difference is the top term, which leads us to 10/5 = 2 as a result

When combined you can see that if you take 5/3x^(-1/3) out, then the first factor remains as x, the second factor remains as 2, and the sign between them is "-".

Conclusion: 5/3[x^(2/3)] - 10/3[x^(-1/3)] = 5/3x^(-1/3) * (x-2) = x * 5/3x^(-1/3) - 2 * 5/3x^(-1/3) = 5/3[x^(2/3)] - 10/3[x^(-1/3)] TRUE. Q.E.D.

[gh0st]

Thanks I also did it by myself just a minute ago it is hard ? Well after all it's precalculus algebra not high school :p

[Axon]

Is this is your homework, because I noticed you always post math questions and asking for help.

[Mordred]

Hard? No, I actually solved it instantly in my head.
I'm not actually even bragging. If you intend to deepen your study of mathematics I suggest you prepare yourself for some of the most difficult problems and theoretical concepts in the whole Universe.