Evaluate
-\frac{1}{\left(x-2\right)\left(x-1\right)}
Expand
-\frac{1}{\left(x-2\right)\left(x-1\right)}
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\frac{\left(2x^{2}-3x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)}-\frac{\left(2x^{2}-5x+3\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and x-2 is \left(x-2\right)\left(x-1\right). Multiply \frac{2x^{2}-3x+2}{x-1} times \frac{x-2}{x-2}. Multiply \frac{2x^{2}-5x+3}{x-2} times \frac{x-1}{x-1}.
\frac{\left(2x^{2}-3x+2\right)\left(x-2\right)-\left(2x^{2}-5x+3\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)}
Since \frac{\left(2x^{2}-3x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)} and \frac{\left(2x^{2}-5x+3\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{2x^{3}-4x^{2}-3x^{2}+6x+2x-4-2x^{3}+2x^{2}+5x^{2}-5x-3x+3}{\left(x-2\right)\left(x-1\right)}
Do the multiplications in \left(2x^{2}-3x+2\right)\left(x-2\right)-\left(2x^{2}-5x+3\right)\left(x-1\right).
\frac{-1}{\left(x-2\right)\left(x-1\right)}
Combine like terms in 2x^{3}-4x^{2}-3x^{2}+6x+2x-4-2x^{3}+2x^{2}+5x^{2}-5x-3x+3.
\frac{-1}{x^{2}-3x+2}
Expand \left(x-2\right)\left(x-1\right).
\frac{\left(2x^{2}-3x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)}-\frac{\left(2x^{2}-5x+3\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and x-2 is \left(x-2\right)\left(x-1\right). Multiply \frac{2x^{2}-3x+2}{x-1} times \frac{x-2}{x-2}. Multiply \frac{2x^{2}-5x+3}{x-2} times \frac{x-1}{x-1}.
\frac{\left(2x^{2}-3x+2\right)\left(x-2\right)-\left(2x^{2}-5x+3\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)}
Since \frac{\left(2x^{2}-3x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)} and \frac{\left(2x^{2}-5x+3\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{2x^{3}-4x^{2}-3x^{2}+6x+2x-4-2x^{3}+2x^{2}+5x^{2}-5x-3x+3}{\left(x-2\right)\left(x-1\right)}
Do the multiplications in \left(2x^{2}-3x+2\right)\left(x-2\right)-\left(2x^{2}-5x+3\right)\left(x-1\right).
\frac{-1}{\left(x-2\right)\left(x-1\right)}
Combine like terms in 2x^{3}-4x^{2}-3x^{2}+6x+2x-4-2x^{3}+2x^{2}+5x^{2}-5x-3x+3.
\frac{-1}{x^{2}-3x+2}
Expand \left(x-2\right)\left(x-1\right).
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