Question

Differentiate

f(x)=(6-5x-x^2)/(x^2-1)

Answer 1

Well, we can factor both the top and bottom:
6 - 5x - x^2 = -x^2 - 5x + 6 = -(x^2+5x - 6)
This then factors into -(x+6)(x-1)

Now the bottom is a difference of squares and simply factors into

(x+1)(x-1), meanign we have:

\[\frac{ -(x+6)(x-1) }{ (x+1)(x-1) }= \frac{ -(x+6) }{ (x+1) }\]
Now we still have to do quotient rule, but this makes the differentiation simpler. Do you know the formula for the quotient rule?

Answer 2

I do, thanks!

Answer 3

Okay, cool. Try it out and see what ya get :3