Differentiation help

Question

anonymous · Answer

$$\LARGE \frac{d}{dx}(\frac{x^4+x^2+1}{x^2-x+1})=\lambda x+c$$
then find $$\LARGE \lambda$$

rational · Answer

integrate both sides

anonymous · Answer

It would be easier to differentiate the left side.

anonymous · Answer

Well -- I suppose you could really do either.

anonymous · Answer

"easy to differentiate LHS" are u serious?

anonymous · Answer

It's a simple application of the quotient rule.  The fact that there are three terms makes it look longer, but it isn't any harder.

anonymous · Answer

If the algebra scares you, then go the other route and integrate both sides.

anonymous · Answer

it is impossible to simplify after differentiation

anonymous · Answer

That's what I meant about the algebra being tedious.  It's not hard to do, it's just irritating to simplify.  So integrate it.

anonymous · Answer

With that being said, if you know how to divide polynomials, that's how I would do it before taking the derivative.

rational · Answer

after integrating simply compare coefficients and solve c and lanbda