Write the correct alternative in the following:
If $y=\frac{a x+b}{x^{2}+c}$, then $\left(2 x y_{1}+y\right) y_{3}=$
A. $3\left(x y_{2}+y_{1}\right) y_{2}$
B. $3\left(x y_{2}+y_{2}\right) y_{2}$
C. $3\left(x y_{2}+y_{1}\right) y_{1}$
D. none of these
Given:
$y=\frac{a x+b}{x^{2}+c}$
$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{a}\left(\mathrm{x}^{2}+\mathrm{c}\right)-2 \mathrm{x}(\mathrm{ax}+\mathrm{b})}{\left(\mathrm{x}^{2}+\mathrm{c}\right)^{2}}$
$=\frac{-a x^{2}-2 b x+a c}{\left(x^{2}+c\right)^{2}}$
$2 x y_{1}=\frac{-a x^{3}-2 b x^{2}+a c x}{\left(x^{2}+c\right)^{2}}$
$\frac{d^{2} y}{d x^{2}}=\frac{(-2 a x-2 b)\left(x^{2}+c\right)^{2}-2(2 x)\left(x^{2}+c\right)\left(-a x^{2}-2 b x+a c\right)}{\left(x^{2}+c\right)^{4}}$
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