Evaluate
\frac{\left(10-x\right)x^{2}}{\left(x-3\right)\left(3x-2\right)}
Expand
\frac{10x^{2}-x^{3}}{\left(x-3\right)\left(3x-2\right)}
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\frac{\left(x^{2}+x-3\right)\left(3x-2\right)}{\left(x-3\right)\left(3x-2\right)}-\frac{\left(4x^{2}+3x-2\right)\left(x-3\right)}{\left(x-3\right)\left(3x-2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and 3x-2 is \left(x-3\right)\left(3x-2\right). Multiply \frac{x^{2}+x-3}{x-3} times \frac{3x-2}{3x-2}. Multiply \frac{4x^{2}+3x-2}{3x-2} times \frac{x-3}{x-3}.
\frac{\left(x^{2}+x-3\right)\left(3x-2\right)-\left(4x^{2}+3x-2\right)\left(x-3\right)}{\left(x-3\right)\left(3x-2\right)}
Since \frac{\left(x^{2}+x-3\right)\left(3x-2\right)}{\left(x-3\right)\left(3x-2\right)} and \frac{\left(4x^{2}+3x-2\right)\left(x-3\right)}{\left(x-3\right)\left(3x-2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{3}-2x^{2}+3x^{2}-2x-9x+6-4x^{3}+12x^{2}-3x^{2}+9x+2x-6}{\left(x-3\right)\left(3x-2\right)}
Do the multiplications in \left(x^{2}+x-3\right)\left(3x-2\right)-\left(4x^{2}+3x-2\right)\left(x-3\right).
\frac{-x^{3}+10x^{2}}{\left(x-3\right)\left(3x-2\right)}
Combine like terms in 3x^{3}-2x^{2}+3x^{2}-2x-9x+6-4x^{3}+12x^{2}-3x^{2}+9x+2x-6.
\frac{-x^{3}+10x^{2}}{3x^{2}-11x+6}
Expand \left(x-3\right)\left(3x-2\right).
\frac{\left(x^{2}+x-3\right)\left(3x-2\right)}{\left(x-3\right)\left(3x-2\right)}-\frac{\left(4x^{2}+3x-2\right)\left(x-3\right)}{\left(x-3\right)\left(3x-2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and 3x-2 is \left(x-3\right)\left(3x-2\right). Multiply \frac{x^{2}+x-3}{x-3} times \frac{3x-2}{3x-2}. Multiply \frac{4x^{2}+3x-2}{3x-2} times \frac{x-3}{x-3}.
\frac{\left(x^{2}+x-3\right)\left(3x-2\right)-\left(4x^{2}+3x-2\right)\left(x-3\right)}{\left(x-3\right)\left(3x-2\right)}
Since \frac{\left(x^{2}+x-3\right)\left(3x-2\right)}{\left(x-3\right)\left(3x-2\right)} and \frac{\left(4x^{2}+3x-2\right)\left(x-3\right)}{\left(x-3\right)\left(3x-2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{3}-2x^{2}+3x^{2}-2x-9x+6-4x^{3}+12x^{2}-3x^{2}+9x+2x-6}{\left(x-3\right)\left(3x-2\right)}
Do the multiplications in \left(x^{2}+x-3\right)\left(3x-2\right)-\left(4x^{2}+3x-2\right)\left(x-3\right).
\frac{-x^{3}+10x^{2}}{\left(x-3\right)\left(3x-2\right)}
Combine like terms in 3x^{3}-2x^{2}+3x^{2}-2x-9x+6-4x^{3}+12x^{2}-3x^{2}+9x+2x-6.
\frac{-x^{3}+10x^{2}}{3x^{2}-11x+6}
Expand \left(x-3\right)\left(3x-2\right).
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