Relatively easy simplification

[thrill3rnit3]

Homework Statement

Simplify

Homework Equations

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

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.

 

[Redbelly98]

Can you factor (a²-a) ?

 

[thrill3rnit3]

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

 

[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

 

[Redbelly98]

What is the common factor in a²-a?

 

[thrill3rnit3]

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