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
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
?
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 =
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?