Question

What is the simplified form of the quantity 9 x squared minus 25 over the quantity 3 x plus 5?

Answer 1

https://gyazo.com/660e4524c7935264f2b85dc266e776c8 what the equation looks like

Answer 2

The numerator is a conjugate:
\[9x ^{2}-25 = (3x + 5)(3x - 5)\]
Now look at your denominator. What happens when a term is divided by its identical self? @Ikou

Answer 3

would it equal zero?

Answer 4

Not quite. What is any number divided by the same number?

For example:
\[\frac{ 2 }{ 2 } = ~?\]

Answer 5

1?

Answer 6

Precisely. Likewise:
\[\frac{ 3x + 5 }{ 3x + 5 } = ~?\]

Answer 7

it would equal one

Answer 8

Exactly. Nice job. What happens when you multiply by one?
\[1 \times (3x - 5) = ~?\]

Answer 9

It's still gonna be 3x-5

Answer 10

You hit the jackpot @Ikou. That's the simplified form of your initial expression. ^_^

Answer 11

Oh oki, so which one would be the answer exactly? https://gyazo.com/c1fd2eb916e5d6238ca0ed15f9a3c09b

Answer 12

Okay, the 'restriction' those are referring to is the denominator. Specifically, when the denominator becomes zero, the entire function is considered undefined. So, to find this value, we take our denominator (3x + 5) from the original equation and equate that to zero. Like this:
\[3x + 5 = 0\]
Solve for x.
\[x = -\frac{ 5 }{ 3 }\]
Which means that for our function:
\[x \neq -\frac{ 5 }{ 3 }\]
This is our restriction.

Answer 13

Did I cross out the answer?

Answer 14

I crossed out all the '+'

Answer 15

Nope, you left it open. It's C. You need the 3x-5 we got earlier and the restriction x cannot equal -5/3.

Answer 16

Oh okii, well thank you for all your help!

Answer 17

You're welcome