hey guys theres this one question ive been working on forever ..

its an index law question

i understand anything rooted is to the power of a half and i am absolutely clueless as to how to advance in this question .. everything else i can do fin except this one question

thanks guys ..

BTW the back of book answer is : x(x-1)^-0.5

2. Originally Posted by jimzer
hey guys

ive been working on this question for more than a day and i can do all others except this single one ..

simplify : <refer to attachment>

i understand anything rooted is to the power of negative 1/2 but i seriously cannot figure this question out ..

the back of book answers is : x(x-1)^0.5

thanks a lot guys
Get a common denominator:

$\frac{1}{\sqrt{x-1}} + \sqrt{x-1} = \frac{1}{\sqrt{x-1}} + \frac{\sqrt{x-1} \cdot \sqrt{x-1}}{\sqrt{x-1}}$

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

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

3. Originally Posted by mr fantastic
Get a common denominator:

$\frac{1}{\sqrt{x-1}} + \sqrt{x-1} = \frac{1}{\sqrt{x-1}} + \frac{\sqrt{x-1} \cdot \sqrt{x-1}}{\sqrt{x-1}}$

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

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