Relatively easy simplification

1. Oct 7, 2008

thrill3rnit3

1. The problem statement, all variables and given/known data

Simplify

2. Relevant equations

$$\frac{\sqrt{a-\sqrt{a}}\times\sqrt{a+\sqrt{a}}}{\sqrt{a-1}}$$

3. The attempt at a solution

$$\frac{\sqrt{(a-\sqrt{a})(a+\sqrt{a})}}{\sqrt{a-1}}$$

$$\frac{\sqrt{a^2-a}}{\sqrt{a-1}} \times \frac{\sqrt{a-1}}{\sqrt{a-1}}$$

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

I'm not sure how to go from there, or if I did something wrong along the way. I just need that next step. thanks.

2. Oct 7, 2008

Redbelly98

Staff Emeritus
Can you factor (a2-a) ?

3. Oct 7, 2008

thrill3rnit3

well if I factor $$(a^2-a)$$, the numerator will just go back to the original expression times $$(a-1)$$, right?

4. Oct 7, 2008

rock.freak667

From here:

$$\frac{\sqrt{a^2-a}}{\sqrt{a-1}}$$

You don't need to multiply by anything, you just need to factor a2-a

5. Oct 7, 2008

Redbelly98

Staff Emeritus
What is the common factor in a2-a?

6. Oct 7, 2008

thrill3rnit3

lol I'm laughing at myself right now...