Question

Can someone help me with this question. I need it thoroughly explained and broken down

Answer 1

Fan and Medal!!!

Answer 2

sure I can explain it if you would like me to.

Answer 3

If you can explain step by step that would be great

Answer 4

let's start off with the first expression:
you probably can see that the (x+3) terms cancel each other out right?

Answer 5

yes

Answer 6

so we now have: \[\frac {x^{2}-9}{x-3} \]
do you recognize something interesting about the numerator of this expression?

Answer 7

yeah its the same as the numerator on the second half

Answer 8

well no (what do you mean actually?)...the thing that I was pointing out is that is a "difference of squares" ever heard of that?

Answer 9

im talking about the other part of the same equation we're doing. but yeah ive heard of that

Answer 10

Oh I see, so what can we do with a difference of squares?

Answer 11

combine them?

Answer 12

\(\bf \cfrac{\cancel{ (x+3) }}{(x-3)}\times \cfrac{(x^2-9)}{\cancel{(x+3) }}\qquad
\begin{cases}
a^2-b^2 = (a-b)(a+b)
\\ \quad \\
\bf x^2-9\to x^2-3^2\to (\square -\square )(\square +\square )
\end{cases}
\\ \quad \\
\cfrac{(\square -\square )(\square +\square )}{(x-3)}?\)

Answer 13

Just the opposite actually! We can expand it out by factoring thusly: \[x^{2} - 9 = (x+3)(x-3)\]
this works for all difference of squares so:
\[x^{2} - 16 = (x+4)(x-4)\]

does that make sense?

Answer 14

kinda..

Answer 15

alright let me ask you: what does this factor into?
\[4x^{2} - 100\]

Answer 16

i dont know ?

Answer 17

well take the first term: 4x^2 and square root it

Answer 18

nvm thanks

Answer 19

wait for the whole thing? or for the difference of squares thing?

Answer 20

the whole thing. youre just confusing me even more

Answer 21

\(\bf \cfrac{\cancel{ (x+3) }}{(x-3)}\times \cfrac{(x^2-9)}{\cancel{(x+3) }}\qquad
\begin{cases}
a^2-b^2 = (a-b)(a+b)
\\ \quad \\
\bf x^2-9\to x^2-3^2\to (\square -\square )(\square +\square )
\end{cases}
\\ \quad \\
\cfrac{(\square -\square )(\square +\square )}{(x-3)}?\)

any ideas on what the "blanks" are ?

Answer 22

Oh I'm sorry. If you could let me know what part you are confused about I can try to amend my explanation or you could just let jdoe explain

Answer 23

keep in mind that's just a difference of squares... thus \(\Large \bf {\color{blue}{ a^2-b^2 = (a-b)(a+b)}}\)