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