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