Find the derivative of h(x)=(x²-x-12)/(x²+25)

So I know the functions factor out to be (x+3)(x−4)/(x²+25)

So far I have this
[(x²+25)(2x - 1)]-[(x²-x-12)(2x )] / (x²+25)²

I seriously don't even know if this is right? What steps proceed after?? I have no clue I tried to figure it out and it went completely wrong! I am so stuck on the derivatives. This is my last resort, can anyone show me how this should be answered correctly? My brain is fried...

Question

Find the derivative of h(x)=(x²-x-12)/(x²+25) 

So I know the functions factor out to be (x+3)(x−4)/(x²+25) 

So far I have this 
[(x²+25)(2x - 1)]-[(x²-x-12)(2x )] / (x²+25)² 

I seriously don't even know if this is right? What steps proceed after?? I have no clue I tried to figure it out and it went completely wrong! I am so stuck on the derivatives. This is my last resort, can anyone show me how this should be answered correctly? My brain is fried...

anonymous · Answer

from what i have learned you need to bring that bottom term to the numerator.

anonymous · Answer

d(u/v)/dx=(u'v-v'u)/v²

u'v=(2x-1)(x²+25)
vu'=2x(x²-x-12)
v²=x^4+50x²+625

Simplify as required

cggurumanjunath · Answer

what you have done is perfectly alright @Ikushinkan .