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\frac{\frac{x}{x}-\frac{3}{x}+\frac{2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.
\frac{\frac{x-3}{x}+\frac{2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
Since \frac{x}{x} and \frac{3}{x} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{\left(x-3\right)x}{x^{2}}+\frac{2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{x-3}{x} times \frac{x}{x}.
\frac{\frac{\left(x-3\right)x+2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
Since \frac{\left(x-3\right)x}{x^{2}} and \frac{2}{x^{2}} have the same denominator, add them by adding their numerators.
\frac{\frac{x^{2}-3x+2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
Do the multiplications in \left(x-3\right)x+2.
\frac{\frac{x^{2}-3x+2}{x^{2}}}{\frac{x}{x^{2}}-\frac{2}{x^{2}}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{1}{x} times \frac{x}{x}.
\frac{\frac{x^{2}-3x+2}{x^{2}}}{\frac{x-2}{x^{2}}}
Since \frac{x}{x^{2}} and \frac{2}{x^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{\left(x^{2}-3x+2\right)x^{2}}{x^{2}\left(x-2\right)}
Divide \frac{x^{2}-3x+2}{x^{2}} by \frac{x-2}{x^{2}} by multiplying \frac{x^{2}-3x+2}{x^{2}} by the reciprocal of \frac{x-2}{x^{2}}.
\frac{x^{2}-3x+2}{x-2}
Cancel out x^{2} in both numerator and denominator.
\frac{\left(x-2\right)\left(x-1\right)}{x-2}
Factor the expressions that are not already factored.
x-1
Cancel out x-2 in both numerator and denominator.
\frac{\frac{x}{x}-\frac{3}{x}+\frac{2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.
\frac{\frac{x-3}{x}+\frac{2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
Since \frac{x}{x} and \frac{3}{x} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{\left(x-3\right)x}{x^{2}}+\frac{2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{x-3}{x} times \frac{x}{x}.
\frac{\frac{\left(x-3\right)x+2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
Since \frac{\left(x-3\right)x}{x^{2}} and \frac{2}{x^{2}} have the same denominator, add them by adding their numerators.
\frac{\frac{x^{2}-3x+2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
Do the multiplications in \left(x-3\right)x+2.
\frac{\frac{x^{2}-3x+2}{x^{2}}}{\frac{x}{x^{2}}-\frac{2}{x^{2}}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{1}{x} times \frac{x}{x}.
\frac{\frac{x^{2}-3x+2}{x^{2}}}{\frac{x-2}{x^{2}}}
Since \frac{x}{x^{2}} and \frac{2}{x^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{\left(x^{2}-3x+2\right)x^{2}}{x^{2}\left(x-2\right)}
Divide \frac{x^{2}-3x+2}{x^{2}} by \frac{x-2}{x^{2}} by multiplying \frac{x^{2}-3x+2}{x^{2}} by the reciprocal of \frac{x-2}{x^{2}}.
\frac{x^{2}-3x+2}{x-2}
Cancel out x^{2} in both numerator and denominator.
\frac{\left(x-2\right)\left(x-1\right)}{x-2}
Factor the expressions that are not already factored.
x-1
Cancel out x-2 in both numerator and denominator.