Simplify equation w/rational exponents

[mnymoen]

Could someone point me in the right direction?
I am trying to simplify (x-1)^1/2(x+2)^4/3 + (x-1)^3/2(x+2)^1/3
I tried lcd on all the exponents but I'm not sure where to go from there.

 

[pka]

Could someone point me in the right direction?
I am trying to simplify (x-1)^1/2(x+2)^4/3 + (x-1)^3/2(x+2)^1/3
I tried lcd on all the exponents but I'm not sure where to go from there.

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

 

[mmm4444bot]

I tried lcd on all the exponents

This statement is not clear; next time, please show us what you tried.

I'm guessing that the instruction to simplify the given expression implies that you're supposed to factor it.

(x - 1)^(1/2) * (x + 2)^(4/3) + (x - 1)^(3/2) * (x + 2)^(1/3)


Note the plus sign highlighted in red.

One factor of (x - 1)^(1/2) appears on the left side of this plus sign, and three factors appear on the right.

Factor out the expression (x - 1)^(1/2).

Four factors of (x + 2)^(4/3) appear on the left side of this plus sign, and one factor appears on the right.

Factor out the expression (x + 2)^(1/3).

Simplify the result.

 

[mnymoen]

Thanks

Thanks for your help. I think I understand now.