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\frac{x}{x-3}+\frac{9-6x}{x\left(x-3\right)}
Factor x^{2}-3x.
\frac{xx}{x\left(x-3\right)}+\frac{9-6x}{x\left(x-3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and x\left(x-3\right) is x\left(x-3\right). Multiply \frac{x}{x-3} times \frac{x}{x}.
\frac{xx+9-6x}{x\left(x-3\right)}
Since \frac{xx}{x\left(x-3\right)} and \frac{9-6x}{x\left(x-3\right)} have the same denominator, add them by adding their numerators.
\frac{x^{2}+9-6x}{x\left(x-3\right)}
Do the multiplications in xx+9-6x.
\frac{\left(x-3\right)^{2}}{x\left(x-3\right)}
Factor the expressions that are not already factored in \frac{x^{2}+9-6x}{x\left(x-3\right)}.
\frac{x-3}{x}
Cancel out x-3 in both numerator and denominator.
\frac{x}{x-3}+\frac{9-6x}{x\left(x-3\right)}
Factor x^{2}-3x.
\frac{xx}{x\left(x-3\right)}+\frac{9-6x}{x\left(x-3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and x\left(x-3\right) is x\left(x-3\right). Multiply \frac{x}{x-3} times \frac{x}{x}.
\frac{xx+9-6x}{x\left(x-3\right)}
Since \frac{xx}{x\left(x-3\right)} and \frac{9-6x}{x\left(x-3\right)} have the same denominator, add them by adding their numerators.
\frac{x^{2}+9-6x}{x\left(x-3\right)}
Do the multiplications in xx+9-6x.
\frac{\left(x-3\right)^{2}}{x\left(x-3\right)}
Factor the expressions that are not already factored in \frac{x^{2}+9-6x}{x\left(x-3\right)}.
\frac{x-3}{x}
Cancel out x-3 in both numerator and denominator.