ShmoopTube

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Sorry And here's your shmoop du jour brought to you

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by birthday clowns Don't worry about it when you see

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one of them crying in his van after the party

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That's just how clowns express joy which of the following

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is equivalent tio this times this and here the potential

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answers ugly All right well this is the type of

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problems we like to call a birthday clown It looks

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terrifying at first but once you give it a chance

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well it's not so bad This thing is seriously ugly

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though and we can pretty it up with minimal effort

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Really just a factoring exercise Each of these polynomial can

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be broken down and factored And once we've done that

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we'll be able to cancel out numbers like nobody's business

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So yeah let's get started a sap so we don't

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have to look at this thing anymore The polynomial in

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the numerator on the left hand side x squared minus

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for x minus twelve will factor into the quantity x

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minus six and the quantity x plus two the other

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numerator x squared plus two x minus fifteen factors into

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the quantity x plus five and quantity x minus three

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Well first denominator x squared plus seven x plus ten

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factories into the quantity x plus five and quantity x

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plus two and finally the other denominator x squared minus

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eight Acts plus 12 factor's india the quantity x minus

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six and the quantity x minus two remember the key

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is to think of the possible factors of the last

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term in the polynomial and then think about how you

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could get to that middle term by either subtracting or

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adding those factors together Well things get slightly trickier when

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there's a coefficient other than one in front of the

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first term But fortunately we don't have to worry about

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that here So for example with the first polynomial we

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know twelve is gonna factor into twelve and one and

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six and two or four and three but only by

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factoring into six and two can we get to the

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four coefficient of the ex term And just like that

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we're starting to see all this nastiness melt away Yeah

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it's just like the end of frozen Now comes the

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easy and fun part because we're multiplying these two fractions

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together we can simplify from one uber long numerator and

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one uber Long denominator and then cancel anything we see

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on both top and bottom which is just about everything

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right So the x minus six goes the x plus

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two goes and the expos five is out of here

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as well leaving just ex ministry over x minus two

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which can't be simplified any further and conveniently enough That's

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option a Okay so maybe you do your next birthday

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at six flags Instead you're getting too old for clowns 00:02:31.97 --> [endTime] anyway Boy there he goes

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