Evaluate
\frac{2\left(x+2\right)}{x^{2}+2x+4}
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\frac{2\left(x+2\right)}{x^{2}+2x+4}
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\frac{\left(x-2\right)\left(x^{2}+2x+4\right)}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}+\frac{\left(x+2\right)\left(x^{2}-2x+4\right)}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}+\frac{16}{x^{4}+4x^{2}+16}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2}-2x+4 and x^{2}+2x+4 is \left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right). Multiply \frac{x-2}{x^{2}-2x+4} times \frac{x^{2}+2x+4}{x^{2}+2x+4}. Multiply \frac{x+2}{x^{2}+2x+4} times \frac{x^{2}-2x+4}{x^{2}-2x+4}.
\frac{\left(x-2\right)\left(x^{2}+2x+4\right)+\left(x+2\right)\left(x^{2}-2x+4\right)}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}+\frac{16}{x^{4}+4x^{2}+16}
Since \frac{\left(x-2\right)\left(x^{2}+2x+4\right)}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)} and \frac{\left(x+2\right)\left(x^{2}-2x+4\right)}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)} have the same denominator, add them by adding their numerators.
\frac{x^{3}+2x^{2}+4x-2x^{2}-4x-8+x^{3}-2x^{2}+4x+2x^{2}-4x+8}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}+\frac{16}{x^{4}+4x^{2}+16}
Do the multiplications in \left(x-2\right)\left(x^{2}+2x+4\right)+\left(x+2\right)\left(x^{2}-2x+4\right).
\frac{2x^{3}}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}+\frac{16}{x^{4}+4x^{2}+16}
Combine like terms in x^{3}+2x^{2}+4x-2x^{2}-4x-8+x^{3}-2x^{2}+4x+2x^{2}-4x+8.
\frac{2x^{3}}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}+\frac{16}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}
Factor x^{4}+4x^{2}+16.
\frac{2x^{3}+16}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}
Since \frac{2x^{3}}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)} and \frac{16}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)} have the same denominator, add them by adding their numerators.
\frac{2\left(x+2\right)\left(x^{2}-2x+4\right)}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}
Factor the expressions that are not already factored in \frac{2x^{3}+16}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}.
\frac{2\left(x+2\right)}{x^{2}+2x+4}
Cancel out x^{2}-2x+4 in both numerator and denominator.
\frac{2x+4}{x^{2}+2x+4}
Use the distributive property to multiply 2 by x+2.
\frac{\left(x-2\right)\left(x^{2}+2x+4\right)}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}+\frac{\left(x+2\right)\left(x^{2}-2x+4\right)}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}+\frac{16}{x^{4}+4x^{2}+16}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2}-2x+4 and x^{2}+2x+4 is \left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right). Multiply \frac{x-2}{x^{2}-2x+4} times \frac{x^{2}+2x+4}{x^{2}+2x+4}. Multiply \frac{x+2}{x^{2}+2x+4} times \frac{x^{2}-2x+4}{x^{2}-2x+4}.
\frac{\left(x-2\right)\left(x^{2}+2x+4\right)+\left(x+2\right)\left(x^{2}-2x+4\right)}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}+\frac{16}{x^{4}+4x^{2}+16}
Since \frac{\left(x-2\right)\left(x^{2}+2x+4\right)}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)} and \frac{\left(x+2\right)\left(x^{2}-2x+4\right)}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)} have the same denominator, add them by adding their numerators.
\frac{x^{3}+2x^{2}+4x-2x^{2}-4x-8+x^{3}-2x^{2}+4x+2x^{2}-4x+8}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}+\frac{16}{x^{4}+4x^{2}+16}
Do the multiplications in \left(x-2\right)\left(x^{2}+2x+4\right)+\left(x+2\right)\left(x^{2}-2x+4\right).
\frac{2x^{3}}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}+\frac{16}{x^{4}+4x^{2}+16}
Combine like terms in x^{3}+2x^{2}+4x-2x^{2}-4x-8+x^{3}-2x^{2}+4x+2x^{2}-4x+8.
\frac{2x^{3}}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}+\frac{16}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}
Factor x^{4}+4x^{2}+16.
\frac{2x^{3}+16}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}
Since \frac{2x^{3}}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)} and \frac{16}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)} have the same denominator, add them by adding their numerators.
\frac{2\left(x+2\right)\left(x^{2}-2x+4\right)}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}
Factor the expressions that are not already factored in \frac{2x^{3}+16}{\left(x^{2}-2x+4\right)\left(x^{2}+2x+4\right)}.
\frac{2\left(x+2\right)}{x^{2}+2x+4}
Cancel out x^{2}-2x+4 in both numerator and denominator.
\frac{2x+4}{x^{2}+2x+4}
Use the distributive property to multiply 2 by x+2.
Examples
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Matrix
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
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Integration
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Limits
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