Evaluate
\frac{2\left(5+2x-x^{2}\right)}{\left(x+3\right)\left(x^{2}-1\right)}
Differentiate w.r.t. x
\frac{2\left(1+24x+20x^{2}+4x^{3}-x^{4}\right)}{\left(-x-3\right)\left(x+3\right)\left(x^{2}-1\right)^{2}}
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\frac{1}{\left(x+1\right)\left(x+3\right)}+\frac{3}{\left(x-1\right)\left(x+1\right)}-\frac{2}{x+3}
Factor x^{2}+4x+3. Factor x^{2}-1.
\frac{x-1}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}+\frac{3\left(x+3\right)}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}-\frac{2}{x+3}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+1\right)\left(x+3\right) and \left(x-1\right)\left(x+1\right) is \left(x-1\right)\left(x+1\right)\left(x+3\right). Multiply \frac{1}{\left(x+1\right)\left(x+3\right)} times \frac{x-1}{x-1}. Multiply \frac{3}{\left(x-1\right)\left(x+1\right)} times \frac{x+3}{x+3}.
\frac{x-1+3\left(x+3\right)}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}-\frac{2}{x+3}
Since \frac{x-1}{\left(x-1\right)\left(x+1\right)\left(x+3\right)} and \frac{3\left(x+3\right)}{\left(x-1\right)\left(x+1\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{x-1+3x+9}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}-\frac{2}{x+3}
Do the multiplications in x-1+3\left(x+3\right).
\frac{4x+8}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}-\frac{2}{x+3}
Combine like terms in x-1+3x+9.
\frac{4x+8}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}-\frac{2\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-1\right)\left(x+1\right)\left(x+3\right) and x+3 is \left(x-1\right)\left(x+1\right)\left(x+3\right). Multiply \frac{2}{x+3} times \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}.
\frac{4x+8-2\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}
Since \frac{4x+8}{\left(x-1\right)\left(x+1\right)\left(x+3\right)} and \frac{2\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{4x+8-2x^{2}-2x+2x+2}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}
Do the multiplications in 4x+8-2\left(x-1\right)\left(x+1\right).
\frac{4x+10-2x^{2}}{\left(x-1\right)\left(x+1\right)\left(x+3\right)}
Combine like terms in 4x+8-2x^{2}-2x+2x+2.
\frac{4x+10-2x^{2}}{x^{3}+3x^{2}-x-3}
Expand \left(x-1\right)\left(x+1\right)\left(x+3\right).
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}