# Simplifying an Expression with negative exponents

• Jun 9th 2009, 06:28 PM
tarabshort
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!!
• Jun 9th 2009, 06:42 PM
Shyam
Quote:

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!!

See your last step,

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

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

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

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

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

$\displaystyle =\frac{x^2-2}{x^3\sqrt{1-x^2}}$
• Jun 9th 2009, 06:50 PM
VonNemo19
Quote:

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. $\displaystyle 1/2$ or $\displaystyle -1/2$.

Check it out.

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

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

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

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