Challenge problem - 'Flex with X'

[aliuz1]

I was wondering if the following solution would also work:

we have (x^2 + 1)(x+1) and (x+1)^2(x-1)

divide both quantities by (x+1) so we get

x^2 + 1 and (x+1)(x-1)

which translates to

x^2 + 1 and x^2 - 1

Quantity A is bigger.

[tommywallach]

You can divide both columns of a QC question by (x-1) as long as you know two things are true:

1) x isn't 1. If it is, you're dividing both sides by zero, which isn't legal.

2) (x-1) can't be negative. If it could be, then when you divide by (x-1), the "sign" (the secret inequality symbol between the columns) would flip, and you wouldn't know which side was bigger.

-t