1. ## Factor and Simplify

Factor and simplify. Express the answer as a fraction without negative exponents:

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

2. Originally Posted by dc52789
Factor and simplify. Express the answer as a fraction without negative exponents:

2x(2x-1)^(1/2) - 2(2x-1)^(1/2)
$\displaystyle 2x\sqrt{2x-1}-2\sqrt{2x-1}$
than
$\displaystyle =(2x-2)\sqrt{2x-1}$

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

3. Ohh...I just edited my equation because I thought I placed the negative sign on the 1/2 square.

4. Originally Posted by dc52789
Factor and simplify. Express the answer as a fraction without negative exponents:

2x(2x-1)^(-1/2) - 2(2x-1)^(1/2)
$\displaystyle \frac{2x}{\sqrt{2x-1}}-2\sqrt{2x-1}$
$\displaystyle =\frac{2x-2\sqrt{2x-1}\sqrt{2x-1}}{\sqrt{2x-1}}$
$\displaystyle =\frac{2x-4x+2}{\sqrt{2x-1}}$
$\displaystyle =\frac{2-2x}{\sqrt{2x-1}}$
Multiplying numerator and denominator by$\displaystyle (2x-1)^\frac{1}{2}$to convert the negative powers into positive
$\displaystyle =\frac{(2-2x)\sqrt{2x-1}}{{\sqrt{2x-1}}^2}$
$\displaystyle Ans=\frac{2(1-x)(2x-1)^{\frac{1}{2}}}{2x-1}$