If frac{d}{d x}left(frac{1+x^2+x^4}{1+x+x^2}r | vedclass

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(C) We are given the expression $f(x) = \frac{1+x^2+x^4}{1+x+x^2}$.First,we simplify the numerator: $1+x^2+x^4 = (1+x^2)^2 - x^2 = (1+x^2-x)(1+x^2+x)

Vedclass · Accepted Answer

$(2, -1)$

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(C) We are given the expression $f(x) = \frac{1+x^2+x^4}{1+x+x^2}$.First,we simplify the numerator: $1+x^2+x^4 = (1+x^2)^2 - x^2 = (1+x^2-x)(1+x^2+x) = (x^2-x+1)(x^2+x+1)$.Thus,$f(x) = \frac{(x^2-x+1)(x^2+x+1)}{x^2+x+1} = x^2-x+1$.Now,we differentiate $f(x)$ with respect to $x$:$\frac{d}{dx}(x^2-x+1) = 2x-1$.Comparing this with $ax+b$,we get $a=2$ and $b=-1$.Therefore,$(a, b) = (2, -1)$.

If $\frac{d}{d x}\left(\frac{1+x^2+x^4}{1+x+x^2}\right)=a x+b$,then $(a, b)=$

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