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?
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 $\displaystyle 2x^2 - x - 1$
we first need factors of the coefficient of $\displaystyle x^2$, here, that's easy, the only integer factors of 2 are 2 and 1 (technically $\displaystyle \pm 2$ and $\displaystyle \pm 1$, but whatever).
so we set up our brackets and place the factors in the first position:
$\displaystyle (2x + {\color{red}a})(x + {\color{blue}b})$
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 $\displaystyle 2bx + ax = -1x$
after a little consideration, $\displaystyle a = +1$ and $\displaystyle b = -1$ are found to be the correct choices. thus we have:
$\displaystyle 2x^2 - x - 1 = (2x + 1)(x - 1)$