# Math Help - rational exponents

1. ## 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.

$-x^2(x^2+1)(x^2+1)^{-1/2}+(x^2+1)^{-1/2}=?$

2. ## 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*}

3. ## Re: rational exponents

thanks. that makes sense. I was over complicating things.