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Yeah Looks a little something like this We got three

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x plus one plus one over three x minus one

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Alright well after all this work it'd be easy to

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forget what they were asking Like feel what the problem's

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all about anyway We're looking for c plus d and

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they'll be easier to find if we replace nine x

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squared over three x minus one with its quotient Right

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So let's do that C plus de plus one over

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three x minus one sure looks like c plus d

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and three x plus one are best friends So what

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do you think Answer d and a simple hard to

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catch division mistake that could lead to three x minus

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one like in number See Well if you're not a

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huge fan of long division in o who is other

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than a calculator here there's another way to tackle this

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problem But it's kind of error prone to So take

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another quick look at the starting equation We got nine

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x squared over three x minus one equals c plus

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de plus one of three x minus one Well sneaky

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way to create the fraction one over three x minus

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one on the left side of the equation Do this

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not x squared plus one minus one over three ex

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money's one And then we kind of sim fly out

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the ones that we got Nine x squared minus one

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over three x minus one plus one over three x

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minus one walk Adding in subtracting one is the same

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thing is adding zero so it doesn't change the overall

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value of the expression from here Do some quick factoring

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and then i'll get the expression into a form we

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can compare c plus the two and that gets you

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three x plus one times quantity here through x minus

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one over three x minus one plus twenty one over

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three x minus one And then that's what it looks

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like when you simplified terms out Three x plus one

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plus one over three x minus one See we ended

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up in the same position as before Oh and there's

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even a third way to approach this problem If you're

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not asleep yet with plain old algebra just subtract one

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over three x minus one from both sides of the

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equation You know we could have done that That's what

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it would look like and well looks awfully familiar It's

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a bit easier to work with tio Maybe we should

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have started off with this one instead It would've been 00:04:02.635 --> [endTime] a whole lot quicker All right we're done

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