# Thread: Factor and Simplify

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)
If your question is
$2x\sqrt{2x-1}-2\sqrt{2x-1}$
than
$=(2x-2)\sqrt{2x-1}$

$
=(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)
so your question now is
$
\frac{2x}{\sqrt{2x-1}}-2\sqrt{2x-1}
$

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

$
=\frac{2x-4x+2}{\sqrt{2x-1}}

$

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

Multiplying numerator and denominator by $(2x-1)^\frac{1}{2}$to convert the negative powers into positive

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

$

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