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If y=(a x^2)/((x-a)(x-b)(x-c))+(b x)/((x...

If `y=(a x^2)/((x-a)(x-b)(x-c))+(b x)/((x-b)(x-c))+c/(x-c)+1` find `dy/dx`

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\begin{equation} \begin{aligned} &\text { We have } y=\frac{a x^{2}}{(x-a)(x-b)(x-c)} +\frac{b x}{(x-b)(x-c)}+\frac{c}{x-c}+1 \\ &=\frac{a x^{2}}{(x-a)(x-b)(x-c)}+\frac{b x}{(x-b)(x-c)}+\frac{x}{(x-c)}\\ &=\frac{a x^{2}}{(x-a)(x-b)(x-c)}+\frac{b x+x^{2}-b x}{(x-b)(x-c)}\\ &=\frac{a x^{2}}{(x-a)(x-b)(x-c)}+\frac{x^{2}}{(x-b)(x-c)}\\ &=\frac{a x^{2}+x^{3}-a x^{2}}{(x-a)(x-b)(x-c)}\\ &=\frac{x^{3}}{(x-a)(x-b)(x-c)}\\ ...
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