Evaluate
-\frac{x+4}{x\left(x+1\right)}
Expand
-\frac{x+4}{x\left(x+1\right)}
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\frac{\left(x+4\right)\left(-x+2\right)}{x\left(x-2\right)}\times \frac{x-4}{x^{2}-3x-4}
Factor the expressions that are not already factored in \frac{8-2x-x^{2}}{x^{2}-2x}.
\frac{-\left(x-2\right)\left(x+4\right)}{x\left(x-2\right)}\times \frac{x-4}{x^{2}-3x-4}
Extract the negative sign in 2-x.
\frac{-\left(x+4\right)}{x}\times \frac{x-4}{x^{2}-3x-4}
Cancel out x-2 in both numerator and denominator.
\frac{-\left(x+4\right)}{x}\times \frac{x-4}{\left(x-4\right)\left(x+1\right)}
Factor the expressions that are not already factored in \frac{x-4}{x^{2}-3x-4}.
\frac{-\left(x+4\right)}{x}\times \frac{1}{x+1}
Cancel out x-4 in both numerator and denominator.
\frac{-\left(x+4\right)}{x\left(x+1\right)}
Multiply \frac{-\left(x+4\right)}{x} times \frac{1}{x+1} by multiplying numerator times numerator and denominator times denominator.
\frac{-x-4}{x\left(x+1\right)}
To find the opposite of x+4, find the opposite of each term.
\frac{-x-4}{x^{2}+x}
Use the distributive property to multiply x by x+1.
\frac{\left(x+4\right)\left(-x+2\right)}{x\left(x-2\right)}\times \frac{x-4}{x^{2}-3x-4}
Factor the expressions that are not already factored in \frac{8-2x-x^{2}}{x^{2}-2x}.
\frac{-\left(x-2\right)\left(x+4\right)}{x\left(x-2\right)}\times \frac{x-4}{x^{2}-3x-4}
Extract the negative sign in 2-x.
\frac{-\left(x+4\right)}{x}\times \frac{x-4}{x^{2}-3x-4}
Cancel out x-2 in both numerator and denominator.
\frac{-\left(x+4\right)}{x}\times \frac{x-4}{\left(x-4\right)\left(x+1\right)}
Factor the expressions that are not already factored in \frac{x-4}{x^{2}-3x-4}.
\frac{-\left(x+4\right)}{x}\times \frac{1}{x+1}
Cancel out x-4 in both numerator and denominator.
\frac{-\left(x+4\right)}{x\left(x+1\right)}
Multiply \frac{-\left(x+4\right)}{x} times \frac{1}{x+1} by multiplying numerator times numerator and denominator times denominator.
\frac{-x-4}{x\left(x+1\right)}
To find the opposite of x+4, find the opposite of each term.
\frac{-x-4}{x^{2}+x}
Use the distributive property to multiply x by x+1.
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}