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\frac{12}{\frac{\left(x+2\right)x}{x\left(x-3\right)}-\frac{\left(x-4\right)\left(x-3\right)}{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 is x\left(x-3\right). Multiply \frac{x+2}{x-3} times \frac{x}{x}. Multiply \frac{x-4}{x} times \frac{x-3}{x-3}.
\frac{12}{\frac{\left(x+2\right)x-\left(x-4\right)\left(x-3\right)}{x\left(x-3\right)}}
Since \frac{\left(x+2\right)x}{x\left(x-3\right)} and \frac{\left(x-4\right)\left(x-3\right)}{x\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{12}{\frac{x^{2}+2x-x^{2}+3x+4x-12}{x\left(x-3\right)}}
Do the multiplications in \left(x+2\right)x-\left(x-4\right)\left(x-3\right).
\frac{12}{\frac{9x-12}{x\left(x-3\right)}}
Combine like terms in x^{2}+2x-x^{2}+3x+4x-12.
\frac{12x\left(x-3\right)}{9x-12}
Divide 12 by \frac{9x-12}{x\left(x-3\right)} by multiplying 12 by the reciprocal of \frac{9x-12}{x\left(x-3\right)}.
\frac{12x\left(x-3\right)}{3\left(3x-4\right)}
Factor the expressions that are not already factored.
\frac{4x\left(x-3\right)}{3x-4}
Cancel out 3 in both numerator and denominator.
\frac{4x^{2}-12x}{3x-4}
Expand the expression.
\frac{12}{\frac{\left(x+2\right)x}{x\left(x-3\right)}-\frac{\left(x-4\right)\left(x-3\right)}{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 is x\left(x-3\right). Multiply \frac{x+2}{x-3} times \frac{x}{x}. Multiply \frac{x-4}{x} times \frac{x-3}{x-3}.
\frac{12}{\frac{\left(x+2\right)x-\left(x-4\right)\left(x-3\right)}{x\left(x-3\right)}}
Since \frac{\left(x+2\right)x}{x\left(x-3\right)} and \frac{\left(x-4\right)\left(x-3\right)}{x\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{12}{\frac{x^{2}+2x-x^{2}+3x+4x-12}{x\left(x-3\right)}}
Do the multiplications in \left(x+2\right)x-\left(x-4\right)\left(x-3\right).
\frac{12}{\frac{9x-12}{x\left(x-3\right)}}
Combine like terms in x^{2}+2x-x^{2}+3x+4x-12.
\frac{12x\left(x-3\right)}{9x-12}
Divide 12 by \frac{9x-12}{x\left(x-3\right)} by multiplying 12 by the reciprocal of \frac{9x-12}{x\left(x-3\right)}.
\frac{12x\left(x-3\right)}{3\left(3x-4\right)}
Factor the expressions that are not already factored.
\frac{4x\left(x-3\right)}{3x-4}
Cancel out 3 in both numerator and denominator.
\frac{4x^{2}-12x}{3x-4}
Expand the expression.