How to find the range of the given function? 
Find the range of $$f(x)=\dfrac{x^2+14x+9}{x^2+2x+3}$$ where $x\in \mathbb R$ 

I thought of finding derivative but this will get too complicated so i am completely blank.
Thanks in advance!

I think you'd have to find the derivative for this problem. But don't worry, finding the derivative is not as cumbersome as you think. Just use the quotient rule and you'll get something reasonable.
You should get $-\frac{12(x^2+x-2)}{(x^2+2x+3)^2}$ and setting that equal to 0 and solving for $x$ should be straightforward.
