# Thread: Simplifying an Expression with negative exponents

1. ## Simplifying an Expression with negative exponents

-x^3(1-x^2)^-1/2 - 2x(1-x^2)^1/2
--------------------------------------
x^4

This is what I've been doing

-x^3(1-x^2)^-1/2 - 2x(1-x^2)^1/2 x (1-x^2)^1/2
--------------------------------------
x^4 x (1-x^2)^1/2

-x^3-2x(1-x^2)
------------------
x^4 <--------------- This is the part I'm stuck on!!!

How do you continue working this problem?? Thanks in advance for the help!!

2. Originally Posted by tarabshort
-x^3(1-x^2)^-1/2 - 2x(1-x^2)^1/2
--------------------------------------
x^4

This is what I've been doing

-x^3(1-x^2)^-1/2 - 2x(1-x^2)^1/2 x (1-x^2)^1/2
--------------------------------------
x^4 x (1-x^2)^1/2

-x^3-2x(1-x^2)
------------------
x^4 <--------------- This is the part I'm stuck on!!!

How do you continue working this problem?? Thanks in advance for the help!!

$=\frac{-x^3-2x(1-x^2)}{x^4(1-x^2)^{\frac{1}{2}}}$

$=\frac{-x^3-2x+2x^3}{x^4(1-x^2)^{\frac{1}{2}}}$

$=\frac{x^3-2x}{x^4(1-x^2)^{\frac{1}{2}}}$

$=\frac{x(x^2-2)}{x^4(1-x^2)^{\frac{1}{2}}}$

$=\frac{x^2-2}{x^3(1-x^2)^{\frac{1}{2}}}$

$=\frac{x^2-2}{x^3\sqrt{1-x^2}}$

3. Originally Posted by tarabshort
-x^3(1-x^2)^-1/2 - 2x(1-x^2)^1/2
--------------------------------------
x^4

This is what I've been doing

-x^3(1-x^2)^-1/2 - 2x(1-x^2)^1/2 x (1-x^2)^1/2
--------------------------------------
x^4 x (1-x^2)^1/2

-x^3-2x(1-x^2)
------------------
x^4 <--------------- This is the part I'm stuck on!!!

How do you continue working this problem?? Thanks in advance for the help!!
Always factor out the LEAST common factor. That includes negative exponents. So, what's bigger. $1/2$ or $-1/2$.

Check it out.

Factoring out $x(1-x^2)^{-1/2}$ gives

$\frac{x(1-x^2)^{-1/2}[-x^2-2(1-x^2)]}{x^4}$

$=-\frac{x^2+2(1-x^2)}{x^3\sqrt{(1-x^2)}}$

$=-\frac{2}{x^3\sqrt{1-x^2}}$