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$y=\frac{x^3}{x-1}$

It is possible to find out the graph of this function by getting the inflection points, critical values, values at infinity and value of first derivative.

But the process is pretty long. Is there any shortcut to find out the graph of any such function without going through the above prcedures?

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Perhaps doing some functions sum will be easier for you ?

$$\frac{x^3}{x-1}=x^2+\frac{x^2}{x-1}=x^2+x+\frac x{x-1}=x^2+x+1+\frac1{x-1}\ldots ?$$

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