Evaluate
-\frac{x+4}{x^{2}+4x+1}
Expand
-\frac{x+4}{x^{2}+4x+1}
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\frac{\frac{1}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}-1}{x}
Factor \left(2+x\right)^{2}-3.
\frac{\frac{1}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}-\frac{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}}{x}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}.
\frac{\frac{1-\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}}{x}
Since \frac{1}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)} and \frac{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{1-x^{2}-x\sqrt{3}-2x+\sqrt{3}x-1-2x}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}}{x}
Do the multiplications in 1-\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right).
\frac{\frac{-x^{2}-4x}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}}{x}
Combine like terms in 1-x^{2}-x\sqrt{3}-2x+\sqrt{3}x-1-2x.
\frac{-x^{2}-4x}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)x}
Express \frac{\frac{-x^{2}-4x}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}}{x} as a single fraction.
\frac{x\left(-x-4\right)}{x\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}
Factor the expressions that are not already factored.
\frac{-x-4}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}
Cancel out x in both numerator and denominator.
\frac{-x-4}{x^{2}+4x+1}
Expand the expression.
\frac{\frac{1}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}-1}{x}
Factor \left(2+x\right)^{2}-3.
\frac{\frac{1}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}-\frac{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}}{x}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}.
\frac{\frac{1-\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}}{x}
Since \frac{1}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)} and \frac{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{1-x^{2}-x\sqrt{3}-2x+\sqrt{3}x-1-2x}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}}{x}
Do the multiplications in 1-\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right).
\frac{\frac{-x^{2}-4x}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}}{x}
Combine like terms in 1-x^{2}-x\sqrt{3}-2x+\sqrt{3}x-1-2x.
\frac{-x^{2}-4x}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)x}
Express \frac{\frac{-x^{2}-4x}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}}{x} as a single fraction.
\frac{x\left(-x-4\right)}{x\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}
Factor the expressions that are not already factored.
\frac{-x-4}{\left(x-\left(\sqrt{3}-2\right)\right)\left(x-\left(-\sqrt{3}-2\right)\right)}
Cancel out x in both numerator and denominator.
\frac{-x-4}{x^{2}+4x+1}
Expand the expression.
Examples
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{ 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}