I need help simplifying [(A+1)^(1/3)]-{[(A+1)^(-2/3)]*(A-1)}
Easier to the eye: (A+1)^1/3 - [ (A+1)^-2/3 * (A-1) ]
It has been 4 years since I took this stuff. Thanks!
Multply the first term by (A+1)^2/3 , both numerator and denominator.
That will leave you an (A+1)^2/3, in the denominator.
Now, factor out that 1/(A+1)^2/3 term in the first and second terms, and combine the numerators.
To simplify the expression [(A+1)^(1/3)] - {[(A+1)^(-2/3)]*(A-1)}, we can follow these steps:
Step 1: Multiply the first term by (A+1)^(2/3) in both the numerator and the denominator:
[(A+1)^(1/3)] * [(A+1)^(2/3)] / [(A+1)^(2/3)]
This simplifies to:
[(A+1)^(1/3 + 2/3)] / [(A+1)^(2/3)]
[(A+1)^(3/3)] / [(A+1)^(2/3)]
(A+1)^(3/3) is equal to (A+1)^(1), which is simply (A+1).
Therefore, the expression becomes:
(A+1) / [(A+1)^(2/3)]
Step 2: Factor out the 1/(A+1)^(2/3) term in both the numerator and the second term:
(A+1) / [(A+1)^(2/3)] - [(A+1)^(-2/3) * (A-1)] / [(A+1)^(2/3)]
Step 3: Combine the numerators:
(A+1) - [(A+1)^(-2/3) * (A-1)] / [(A+1)^(2/3)]
And that is the simplified form of the given expression.