What is the simplified form of the quantity x^2-81 over the quantity x-9 ?

Question

anonymous · Answer

i know the answer is x-9 but i dont know how to get the restriction

anonymous · Answer

i mean x+9

sburchette · Answer

You can factor x^2-81 as a difference of two squares.  Factoring will yield$$((x-9)(x+9))/(x-9)$$The (x-9) term will cancel on the top and bottom leaving you with (x+9)

anonymous · Answer

i know thats what i got but i dont understand hpw to get the restriction

sburchette · Answer

I'm not sure what you mean by restriction. If it is a function, then $$x \neq9$$Because the original expression was undefined there.

anonymous · Answer

x – 9, with the restriction x ≈ 9
		
x – 9, with the restriction x ≈ –9
		
x + 9, with the restriction x ≈ –9
		
x + 9, with the restriction x ≈ 9

sburchette · Answer

I'd say its the last option because it simplifies to x+9 and x cannot equal 9 because it causes the original expression to be undefined.

anonymous · Answer

ok. im not used to the squiggly equal sign so im not really sure

sburchette · Answer

Usually that means something is approximately equal, I haven't seen it used to state something cannot equal a quantity.