Calculate: limit as x approaches 0 of 3/x+3/(x^2-x)

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Expression: $\lim _{x\to 0}(\frac{3}{x}+\frac{3}{x^{2}-x})$

Multiply by the conjugate of $ \frac{3}{x}+\frac{3}{x^{2}-x}: \frac{\frac{9}{x^{2}}-\frac{9}{x^{4}-2x^{3}+x^{2}}}{\frac{3}{x}-\frac{3}{x^{2}-x}}$

$=\lim _{x\to 0}(\frac{\frac{9}{x^{2}}-\frac{9}{x^{4}-2x^{3}+x^{2}}}{\frac{3}{x}-\frac{3}{x^{2}-x}})$

Simplify $ \frac{\frac{9}{x^{2}}-\frac{9}{x^{4}-2x^{3}+x^{2}}}{\frac{3}{x}-\frac{3}{x^{2}-x}}:{\quad}\frac{3}{x-1}$

$=\lim _{x\to 0}(\frac{3}{x-1})$

Plug in the value $ x=0$

$=\frac{3}{0-1}$

Simplify

$=-3$

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