Evaluate
-\frac{x^{2}+2}{\left(x-5\right)\left(x^{2}-4\right)}
Expand
-\frac{x^{2}+2}{\left(x-5\right)\left(x^{2}-4\right)}
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\frac{x}{\left(x-2\right)\left(x+2\right)}-\frac{2x-1}{\left(x-5\right)\left(x+2\right)}
Factor x^{2}-4. Factor x^{2}-3x-10.
\frac{x\left(x-5\right)}{\left(x-5\right)\left(x-2\right)\left(x+2\right)}-\frac{\left(2x-1\right)\left(x-2\right)}{\left(x-5\right)\left(x-2\right)\left(x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-2\right)\left(x+2\right) and \left(x-5\right)\left(x+2\right) is \left(x-5\right)\left(x-2\right)\left(x+2\right). Multiply \frac{x}{\left(x-2\right)\left(x+2\right)} times \frac{x-5}{x-5}. Multiply \frac{2x-1}{\left(x-5\right)\left(x+2\right)} times \frac{x-2}{x-2}.
\frac{x\left(x-5\right)-\left(2x-1\right)\left(x-2\right)}{\left(x-5\right)\left(x-2\right)\left(x+2\right)}
Since \frac{x\left(x-5\right)}{\left(x-5\right)\left(x-2\right)\left(x+2\right)} and \frac{\left(2x-1\right)\left(x-2\right)}{\left(x-5\right)\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-5x-2x^{2}+4x+x-2}{\left(x-5\right)\left(x-2\right)\left(x+2\right)}
Do the multiplications in x\left(x-5\right)-\left(2x-1\right)\left(x-2\right).
\frac{-x^{2}-2}{\left(x-5\right)\left(x-2\right)\left(x+2\right)}
Combine like terms in x^{2}-5x-2x^{2}+4x+x-2.
\frac{-x^{2}-2}{x^{3}-5x^{2}-4x+20}
Expand \left(x-5\right)\left(x-2\right)\left(x+2\right).
\frac{x}{\left(x-2\right)\left(x+2\right)}-\frac{2x-1}{\left(x-5\right)\left(x+2\right)}
Factor x^{2}-4. Factor x^{2}-3x-10.
\frac{x\left(x-5\right)}{\left(x-5\right)\left(x-2\right)\left(x+2\right)}-\frac{\left(2x-1\right)\left(x-2\right)}{\left(x-5\right)\left(x-2\right)\left(x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-2\right)\left(x+2\right) and \left(x-5\right)\left(x+2\right) is \left(x-5\right)\left(x-2\right)\left(x+2\right). Multiply \frac{x}{\left(x-2\right)\left(x+2\right)} times \frac{x-5}{x-5}. Multiply \frac{2x-1}{\left(x-5\right)\left(x+2\right)} times \frac{x-2}{x-2}.
\frac{x\left(x-5\right)-\left(2x-1\right)\left(x-2\right)}{\left(x-5\right)\left(x-2\right)\left(x+2\right)}
Since \frac{x\left(x-5\right)}{\left(x-5\right)\left(x-2\right)\left(x+2\right)} and \frac{\left(2x-1\right)\left(x-2\right)}{\left(x-5\right)\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-5x-2x^{2}+4x+x-2}{\left(x-5\right)\left(x-2\right)\left(x+2\right)}
Do the multiplications in x\left(x-5\right)-\left(2x-1\right)\left(x-2\right).
\frac{-x^{2}-2}{\left(x-5\right)\left(x-2\right)\left(x+2\right)}
Combine like terms in x^{2}-5x-2x^{2}+4x+x-2.
\frac{-x^{2}-2}{x^{3}-5x^{2}-4x+20}
Expand \left(x-5\right)\left(x-2\right)\left(x+2\right).
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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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