Question

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

• A. (-1,2)
• B. (-2,1)
• C. (2,-1)
• D. (1,2)

Answer 1

Answer: (C)

$ax+b=\frac{d}{dx}\left\{\frac{1+x^2+x^4}{1+x+x^2}\right\}$
$=\frac{d}{dx}\left\{\frac{\left(1+x+x^2\right)\left(1-x+x^2\right)}{1+x+x^2}\right\}$
$=\frac{d}{dx}\left\{1-x+x^2\right\}=-1+2x$
$\Rightarrow a=2,b=-1.$