hi i've been told to do

$\displaystyle \frac {x^2 + 3x + 1}{x + 2}$ and the answer is $\displaystyle x + 1 - \frac{1}{x + 2}$

can someone show me how to arrive at this answer please? thanks

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- Sep 17th 2009, 02:33 AMmarkalgebraic fraction
hi i've been told to do

$\displaystyle \frac {x^2 + 3x + 1}{x + 2}$ and the answer is $\displaystyle x + 1 - \frac{1}{x + 2}$

can someone show me how to arrive at this answer please? thanks - Sep 17th 2009, 02:43 AMmathaddict
- Sep 17th 2009, 02:46 AMGrandadAlgebraic long division
Hello markYou need to use algebraic long division. There's an example here.

See if you can apply this to your example. You should get a quotient $\displaystyle x+1$ and a remainder $\displaystyle -1$. Can you then see what to do with the remainder? (Think about how you handle the remainder when you divide using ordinary numbers.

Grandad - Sep 17th 2009, 02:46 AMmark
not really, thats how the book set it out before putting it in the form i had it in, could you show me from there please?

- Sep 17th 2009, 02:48 AMmark
ok i'll try to figure out how to use the long division

- Sep 17th 2009, 03:04 AMmark
hi could someone please write out the long division to answer this question so i can check my working?

thankyou - Sep 17th 2009, 03:06 AMmark
ah i figured out what math addict means now

- Sep 17th 2009, 03:28 AMpacman
http://www.mathhelpforum.com/math-he...85d3376f-1.gif ?

without latex, ugly result

11111 __x_________

x + 2 / x^2 + 3x + 1

000000__x^2 + 2x__(subtract)

000000000000x + 1 ( bringdown 1)

then next term will be 1

00000__x + 1 0__

x + 2 / x^2 + 3x + 1

__000000x^2 + 2x__(subtract)

000000000000x + 1 ( bringdown 1)

__000000000000x + 2__(subtract)

00000000000000 - 1 ( remainder)

thus http://www.mathhelpforum.com/math-he...85d3376f-1.gif = http://www.mathhelpforum.com/math-he...642de82b-1.gif - Sep 17th 2009, 03:38 AMpacman
**Mathaddict method**is even beautiful,

http://www.mathhelpforum.com/math-he...03b63781-1.gif, how?

x^2 + 3x + 1 = x^2 + 3x + (1 + 2 - 2), you breakdown the 3rd-term

then, rearrange (x^2 + 3x + 2) - 1, you will get

(x + 1)(x + 2) - 1

divide by (x + 2) each term

(x + 1)(x + 2)/(x + 2) - 1/(x + 2), notice the (x + 2) term cancels

thus, (x^2 + 3x + 1)/(x + 2) = (x + 1) - 1/(x + 2).

easy right?