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