Evaluate
\frac{4x^{2}-11x-6}{\left(x-2\right)\left(x+1\right)}
Expand
\frac{4x^{2}-11x-6}{\left(x-2\right)\left(x+1\right)}
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\frac{\left(x-6\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}+\frac{3x\left(x-2\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-2 and x+1 is \left(x-2\right)\left(x+1\right). Multiply \frac{x-6}{x-2} times \frac{x+1}{x+1}. Multiply \frac{3x}{x+1} times \frac{x-2}{x-2}.
\frac{\left(x-6\right)\left(x+1\right)+3x\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}
Since \frac{\left(x-6\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} and \frac{3x\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{x^{2}+x-6x-6+3x^{2}-6x}{\left(x-2\right)\left(x+1\right)}
Do the multiplications in \left(x-6\right)\left(x+1\right)+3x\left(x-2\right).
\frac{4x^{2}-11x-6}{\left(x-2\right)\left(x+1\right)}
Combine like terms in x^{2}+x-6x-6+3x^{2}-6x.
\frac{4x^{2}-11x-6}{x^{2}-x-2}
Expand \left(x-2\right)\left(x+1\right).
\frac{\left(x-6\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}+\frac{3x\left(x-2\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-2 and x+1 is \left(x-2\right)\left(x+1\right). Multiply \frac{x-6}{x-2} times \frac{x+1}{x+1}. Multiply \frac{3x}{x+1} times \frac{x-2}{x-2}.
\frac{\left(x-6\right)\left(x+1\right)+3x\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}
Since \frac{\left(x-6\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} and \frac{3x\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{x^{2}+x-6x-6+3x^{2}-6x}{\left(x-2\right)\left(x+1\right)}
Do the multiplications in \left(x-6\right)\left(x+1\right)+3x\left(x-2\right).
\frac{4x^{2}-11x-6}{\left(x-2\right)\left(x+1\right)}
Combine like terms in x^{2}+x-6x-6+3x^{2}-6x.
\frac{4x^{2}-11x-6}{x^{2}-x-2}
Expand \left(x-2\right)\left(x+1\right).
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Simultaneous equation
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Integration
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Limits
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