# rational exponents

• August 11th 2011, 10:46 PM
skoker
rational exponents
I can not get this. the left hand side simplifies to the right.

$-x^2(x^2+1)^{-3/2}+(x^2+1)^{-1/2} \Rightarrow (x^2+1)^{-3/2}$

I tried this but but then if I factor out (x^2+1) there are extra terms etc.

$-x^2(x^2+1)(x^2+1)^{-1/2}+(x^2+1)^{-1/2}=?$
• August 11th 2011, 11:34 PM
Prove It
Re: rational exponents
\displaystyle \begin{align*} -x^2(x^2 + 1)^{-\frac{3}{2}} + (x^2 +1)^{-\frac{1}{2}} &= \frac{-x^2}{(x^2 + 1)^{\frac{3}{2}}} + \frac{1}{(x^2 + 1)^{\frac{1}{2}}} \\ &= \frac{-x^2}{(x^2 + 1)^{\frac{3}{2}}} + \frac{x^2 + 1}{(x^2 + 1)^{\frac{3}{2}}} \\ &= \frac{-x^2 + x^2 + 1}{(x^2 + 1)^{\frac{3}{2}}} \\ &= \frac{1}{(x^2 + 1)^{\frac{3}{2}}} \\ &= (x^2 + 1)^{-\frac{3}{2}}\end{align*}
• August 11th 2011, 11:41 PM
skoker
Re: rational exponents
thanks. that makes sense. I was over complicating things.