Evaluate
\frac{x^{2}-3x-1}{\left(x-2\right)\left(x+1\right)}
Expand
\frac{x^{2}-3x-1}{x^{2}-x-2}
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1+\frac{1-2x}{\left(x-2\right)\left(x+1\right)}
Factor x^{2}-x-2.
\frac{\left(x-2\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}+\frac{1-2x}{\left(x-2\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\left(x-2\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}.
\frac{\left(x-2\right)\left(x+1\right)+1-2x}{\left(x-2\right)\left(x+1\right)}
Since \frac{\left(x-2\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} and \frac{1-2x}{\left(x-2\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{x^{2}+x-2x-2+1-2x}{\left(x-2\right)\left(x+1\right)}
Do the multiplications in \left(x-2\right)\left(x+1\right)+1-2x.
\frac{x^{2}-3x-1}{\left(x-2\right)\left(x+1\right)}
Combine like terms in x^{2}+x-2x-2+1-2x.
\frac{x^{2}-3x-1}{x^{2}-x-2}
Expand \left(x-2\right)\left(x+1\right).
1+\frac{1-2x}{\left(x-2\right)\left(x+1\right)}
Factor x^{2}-x-2.
\frac{\left(x-2\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}+\frac{1-2x}{\left(x-2\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\left(x-2\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}.
\frac{\left(x-2\right)\left(x+1\right)+1-2x}{\left(x-2\right)\left(x+1\right)}
Since \frac{\left(x-2\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} and \frac{1-2x}{\left(x-2\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{x^{2}+x-2x-2+1-2x}{\left(x-2\right)\left(x+1\right)}
Do the multiplications in \left(x-2\right)\left(x+1\right)+1-2x.
\frac{x^{2}-3x-1}{\left(x-2\right)\left(x+1\right)}
Combine like terms in x^{2}+x-2x-2+1-2x.
\frac{x^{2}-3x-1}{x^{2}-x-2}
Expand \left(x-2\right)\left(x+1\right).
Examples
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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