Thread: Absolute Value algebra manipulation

Hi all,
I have arrived at a question involving absolute value I am unsure of. It involves manipulation of a simple expression, the only problem being the absolute value segment, which I havent come across in this sort of context. See below:

(7x+21) / ((x+5)|x-1|)

if the denominator were (x+5)(x-1) it would be easy (x^2 + 4x - 5). Can I treat |x-1| the same?

I have tried simplifying |x-1| to sqrt((x-1)^2) at which stage the sqrt and '^2' would normally cancel, but isn't this taking away that which makes absolute value unique?

Or am I over thinking this all?

Then,

right, so first of all you isolate the absolute value portion of the equation, then (in the case of the example I gave where I had to find the Horizontal Asymptote) I'd calculate the HA for both denominators listed above? (meaning (x+5)(x-1) and (x+5)(1-x))