Find derivative using Quotient rule

[DollarBill]

Homework Statement

Differentiate

f(x) = 6-5x-x² / x²-1
-------
A) -5-5x / x²-1

B) 5 / (x+1)²

C) -5-5x / (x²-1)²

D) -5 / (x+1)²

E) -5+5x / x²-1

F) None of the above

The Attempt at a Solution

(x²)(-5-2x)-(6-5x-x²)(2x) / (x²-1)²

Simplified to:

5x²-10x+5 / x⁴-2x²+1

But it's not one of the answer choices. I tried simplifying it even further to:

5(x²-2x) / x⁴-2x²+1
or
5(x²-2x) / (x²-1)²

But I can't see where else to go with it.

 

[rocomath]

Ok so you're taking a quiz or exam? So I think it's best to wait till you're done :)

 

[DollarBill]

It actually is just homework

 

[rocomath]

I don't see much homework with multiple choice, so yeah ...

 

[DollarBill]

I don't even get the benefit of the doubt? I can guarantee you that this is just a homework problem.

But if you're not going to believe or help me, can you at least tell me if I'm headed in the right direction or did I miss something?

 

[JG89]

"(x^2)(-5-2x)-(6-5x-x^2)(2x) / (x2-1)^2"

the first (x^2) should be (x^2 - 1)

it could also be possible that the answers you are given are in a simplified form. What are the answers?

 

[DollarBill]

These are the choices:

(A) -5-5x / x2-1

(B) 5 / (x+1)2

(C) -5-5x / (x2-1)2

(D) -5 / (x+1)2

(E) -5+5x / x2-1

(F) None of the above

-------------

Yea, I forgot to put the "-1", but I did do it on my paper.

From:
(x²-1)(-5-2x)-(6-5x-x²)(2x) / (x²-1)²

I got:
-5x²+5-2x³+2x-12x+10x²+2x³ / x⁴-2x²+1

Simplified to:
5x²-10x+5 / x⁴-2x²+1

to

5(x²-2x+1) / (x²-1)²
or
5(x-1)² / (x²-1)²

But I don't know where to go from there

 

[Skatch]

5(x-1)² / (x²-1)² is correct thusfar. Just notice that (x²-1) is a difference of two squares. Change it to (x+1)(x-1) and your answer simplifies to (B), which should be correct.

 

[DollarBill]

I completely missed that. Thanks!