which number(s) cannot be used in the following expressions: a^2-36/a^2+9a+36
a.-3 b.3 c.-6 d.6 e.18 f.-18

Question

which number(s) cannot be used in the following expressions: a^2-36/a^2+9a+36
a.-3  b.3  c.-6  d.6  e.18  f.-18

anonymous · Answer

Numbers that "cannot" be used are ones where the denominator is zero.  In other words, the values of $a$ such that $a^2+9a+36=0$.

anonymous · Answer

i dont understand

anonymous · Answer

Do you agree with me that fractions can't have zero as a denominator?

anonymous · Answer

yes i know that part , so how do i figure out what numbers i cant use?

anonymous · Answer

Do you agree that $\dfrac{a^2-36}{a^2+9a+36}$ is a fraction with denominator $a^2+9a+36$?

anonymous · Answer

If so, the values of $a$ that you cannot use are the ones that make the denominator $a^2+9a+36$ zero, which are the solutions to $a^2+9a+36=0$, which is what I mentioned above.

anonymous · Answer

whats the next step?

anonymous · Answer

Solve $a^2+9a+36=0$.

anonymous · Answer

i dont know how

anonymous · Answer

Start by factoring the left-hand side.

anonymous · Answer

Or, use the quadratic formula if you are really stuck.

anonymous · Answer

i tried to use the quadratic formula i didnt work

anonymous · Answer

The quadratic formula always works, @tbrooks3. ;-)  What did you get?

anonymous · Answer

Ah I see...you probably got a negative under the square root, right?  That means there are no real solutions, which means that the given expression can take in ANY number without restriction.

anonymous · Answer

so a ,c,f ?

anonymous · Answer

What?  No!  None of the answers are correct.  There are NO restrictions.

anonymous · Answer

what does that mean?

anonymous · Answer

None of the answers given are correct.  There is no number $a$ could be that is not allowed.

anonymous · Answer

but i have to pick one of the multiple choice answers

anonymous · Answer

If you don't believe me, look here to see that the domain is all real numbers. http://www.wolframalpha.com/input/?i=(x%5E2-36)%2F(x%5E2%2B9x%2B36) Either the problem is put in wrong, or you copied it wrong. The function you gave doesn't have an answer for the question given.

anonymous · Answer

ohhh your right sorry it should say +18 on the denominator not +36 @yakeyglee

anonymous · Answer

*sigh*...okay so what are the solutions to $a^2+9a+18=0$?

anonymous · Answer

i still have no clue. i have a quadratic calculator but its not working right now

anonymous · Answer

...okay, so do it by hand.  That's an easy one to factor, anyway.  Give it a bit of thought...what numbers sum to 9 and multiply to 18?

anonymous · Answer

6,3

anonymous · Answer

Good...so the factored form is $a^2+9a+18=(a+3)(a+6)=0$.

anonymous · Answer

?

anonymous · Answer

b & c ?