1. algebraic 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

2. Originally Posted by mark
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
Hi

$\displaystyle x^2+3x+1=(x+1)(x+2)-1$

do you see how to go on from here ?

3. Algebraic long division

Hello mark
Originally Posted by mark
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
You 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.

4. 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?

5. ok i'll try to figure out how to use the long division

6. hi could someone please write out the long division to answer this question so i can check my working?

thankyou

7. ah i figured out what math addict means now

8. ?

without latex, ugly result

11111 __x_________
x + 2 / x^2 + 3x + 1
000000x^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 =

9. Mathaddict method is even beautiful,

, 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?