GregMat Quant Problem Query

Hi folks - could someone please help me understand why in this situation, i can’t expand the RHS quantity as (a+b)(a-b) and cancel (a+b) from both LHS and RHS? The values are clearly not 0, and its not an inequality - so why not?
Thanks!

What if a+b was something negative? Is dividing both sides by a negative a safe operation?