1. Limits

I got the question to find limits:

lim(x -> (-0.5)) (((2x^2)-x-1)/(2x+1))

Now im not sure how to start it
could someone help?

2. Factor and see what happens.
$
\frac{{2x^2 - x - 1}}{{2x + 1}} = \frac{{\left( {2x + 1} \right)\left( {x - 1} \right)}}{{\left( {2x + 1} \right)}}$

3. so basically 2x^2 becomes 2x+1?

4. Originally Posted by taurus
so basically 2x^2 becomes 2x+1?
no, he factorized $2x^2 - x - 1$ by foiling.

5. But how can u foil that? bit confused

6. Originally Posted by taurus
But how can u foil that? bit confused
do you know what "foiling" is? if not, you should look it up, it is something you should know how to do long before you do limits.

we have $2x^2 - x - 1$

we first need factors of the coefficient of $x^2$, here, that's easy, the only integer factors of 2 are 2 and 1 (technically $\pm 2$ and $\pm 1$, but whatever).

so we set up our brackets and place the factors in the first position:

$(2x + {\color{red}a})(x + {\color{blue}b})$

now we need to find two numbers, a and b, so that when multiplied they give -1, so that when we expand the brackets, we get back the middle term -x.

here, again, the numbers are easy, 1 and -1 are out numbers, now we just have to figure out what position to put them in. you can do trial and error, but you really want to be able to set them up so that $2bx + ax = -1x$

after a little consideration, $a = +1$ and $b = -1$ are found to be the correct choices. thus we have:

$2x^2 - x - 1 = (2x + 1)(x - 1)$