How Do You Simplify Complex Algebraic Expressions?

[roger12]

Homework Statement

Simplify the following, giving the result without fractional indices:

[(x^2 -1)^2 * √(x+1)]/ (x-1)^3/2

Homework Equations

The Attempt at a Solution

There are no common bases to add the indices and no common indices to multiply out the bases so I tried this and got it wrong, please show me where though:

[(x-1) (x+1)]^2 * (x+1)^(1/2)] / (x-1)^(3/2)

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

multiplied the indices by 2 and got rid of the fractions

=[(x-1)^4 * (x+1)^4 * (x+1)] / (x-1)^3

= (x-1) *(x+1)^5

But my textbook says it is :( x + 1 )^2 √( x^2 - 1 )

Thank You.

 

[lewando]

multiplied the indices by 2 and got rid of the fractions

=[(x-1)^4 * (x+1)^4 * (x+1)] / (x-1)^3

= (x-1) *(x+1)^5

You effectively squared the original problem. Now you need to un-square your result.

 

[HallsofIvy]

"Without fractional indices" just mean you need to use the square root:
$$(x- 1)^{3/2}= \sqrt{(x-1)^3}$$

 

[roger12]

Thank You, Everyone.