Question

(x^2-1)^1/2-(x^2-1)^-1/2(2-x^2)/ x^2-1

Answer 1

\[(x^{2}-1)^{1/2}-(x^{2}-1)^{-1/2}(2-x^{2})/(x^{2}-1)\]
Before I go on, is that what your problem states?

Answer 2

YES

Answer 3

OK... just a moment

Answer 4

First, simplify to something like \[(x^{2}-1)^{1/2}-(x^{2}-1)^{-3/2}(2-x^{2})\]
and let's see what we can factor out...

Answer 5

\[(x^{2}-1)^{1/2}(1-(x^{2}-1)^{3}(2-x^{2}))\]

Answer 6

not done yet... let me write it out on paper first

Answer 7

simplifying inside the parentheses, we get
\[(x^{2}-1)^{1/2}(x^{8}-5x^{6}+9x^{4}-7x^{2}+3)\] which brings us to the last step....

Answer 8

actually, I'm not certain there is another simplification that you can make. Check my work to be sure.

Answer 9

what happened to denominator?

Answer 10

I took \[1/(x^{2}-1) = (x^{2}-1)^{-1}\] to get rid of it

Answer 11

according to the book the answer is \[\pm \sqrt{3/5}\]