Find the derivative and simplify : y=(3x^2+5x+1)/(3-x^2) ?

Question

mertsj · Answer

$$y'=\frac{(3-x^2)(6x+5)-(3x^2+5x+1)(-2x)}{(3-x^2)^2}$$

mertsj · Answer

Probably want to do some algebra on that and clean it up a bit.

s · Answer

I got this derivative, and later i was confused with algebra, and never got the right answer.( should be 5(x+1)(x+3) divided by (3-x^2)^2

mertsj · Answer

Let's work on the numerator then

mertsj · Answer

$$(3-x^2)(6x+5)=18x+15-6x^3-5x^2=-6x^3-5x^2+18x+15$$

mertsj · Answer

Set that aside for a minute while we get
$$-2x(3x^2+5x+1)$$
worked out.

mertsj · Answer

$$-6x^3-10x^2-2x$$

mertsj · Answer

We have to subtract that from the first expression so we will just add the opposite:

mertsj · Answer

$$-6x^3-5x^2+18x+15+6x^3+10x^2+2x=5x^5+20x+15$$

mertsj · Answer

$$5x^2+20x+15=5(x^2+4x+3)=5(x+3)(x+1)$$

mertsj · Answer

So that's the numerator.  Just put it over the denominator.

s · Answer

ooh, now i get that too, probably had a mistake while simplifying. Thank you.Now it makes sense!

mertsj · Answer

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