Ikou
  • Ikou
What is the simplified form of the quantity 9 x squared minus 25 over the quantity 3 x plus 5?
Mathematics
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
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Ikou
  • Ikou
https://gyazo.com/660e4524c7935264f2b85dc266e776c8 what the equation looks like
anonymous
  • anonymous
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
Ikou
  • Ikou
would it equal zero?

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anonymous
  • anonymous
Not quite. What is any number divided by the same number? For example: \[\frac{ 2 }{ 2 } = ~?\]
Ikou
  • Ikou
1?
anonymous
  • anonymous
Precisely. Likewise: \[\frac{ 3x + 5 }{ 3x + 5 } = ~?\]
Ikou
  • Ikou
it would equal one
anonymous
  • anonymous
Exactly. Nice job. What happens when you multiply by one? \[1 \times (3x - 5) = ~?\]
Ikou
  • Ikou
It's still gonna be 3x-5
anonymous
  • anonymous
You hit the jackpot @Ikou. That's the simplified form of your initial expression. ^_^
Ikou
  • Ikou
Oh oki, so which one would be the answer exactly? https://gyazo.com/c1fd2eb916e5d6238ca0ed15f9a3c09b
anonymous
  • anonymous
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.
Ikou
  • Ikou
Did I cross out the answer?
Ikou
  • Ikou
I crossed out all the '+'
anonymous
  • anonymous
Nope, you left it open. It's C. You need the 3x-5 we got earlier and the restriction x cannot equal -5/3.
Ikou
  • Ikou
Oh okii, well thank you for all your help!
anonymous
  • anonymous
You're welcome

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