Evaluate
\frac{9-2x-x^{2}}{x+4}
Expand
\frac{9-2x-x^{2}}{x+4}
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\frac{x+4}{\left(x+4\right)^{2}}-\frac{x^{2}-4}{x+2}
Factor the expressions that are not already factored in \frac{x+4}{x^{2}+8x+16}.
\frac{1}{x+4}-\frac{x^{2}-4}{x+2}
Cancel out x+4 in both numerator and denominator.
\frac{1}{x+4}-\frac{\left(x-2\right)\left(x+2\right)}{x+2}
Factor the expressions that are not already factored in \frac{x^{2}-4}{x+2}.
\frac{1}{x+4}-\left(x-2\right)
Cancel out x+2 in both numerator and denominator.
\frac{1}{x+4}-x+2
To find the opposite of x-2, find the opposite of each term.
\frac{1}{x+4}+\frac{\left(-x+2\right)\left(x+4\right)}{x+4}
To add or subtract expressions, expand them to make their denominators the same. Multiply -x+2 times \frac{x+4}{x+4}.
\frac{1+\left(-x+2\right)\left(x+4\right)}{x+4}
Since \frac{1}{x+4} and \frac{\left(-x+2\right)\left(x+4\right)}{x+4} have the same denominator, add them by adding their numerators.
\frac{1-x^{2}-4x+2x+8}{x+4}
Do the multiplications in 1+\left(-x+2\right)\left(x+4\right).
\frac{9-x^{2}-2x}{x+4}
Combine like terms in 1-x^{2}-4x+2x+8.
\frac{x+4}{\left(x+4\right)^{2}}-\frac{x^{2}-4}{x+2}
Factor the expressions that are not already factored in \frac{x+4}{x^{2}+8x+16}.
\frac{1}{x+4}-\frac{x^{2}-4}{x+2}
Cancel out x+4 in both numerator and denominator.
\frac{1}{x+4}-\frac{\left(x-2\right)\left(x+2\right)}{x+2}
Factor the expressions that are not already factored in \frac{x^{2}-4}{x+2}.
\frac{1}{x+4}-\left(x-2\right)
Cancel out x+2 in both numerator and denominator.
\frac{1}{x+4}-x+2
To find the opposite of x-2, find the opposite of each term.
\frac{1}{x+4}+\frac{\left(-x+2\right)\left(x+4\right)}{x+4}
To add or subtract expressions, expand them to make their denominators the same. Multiply -x+2 times \frac{x+4}{x+4}.
\frac{1+\left(-x+2\right)\left(x+4\right)}{x+4}
Since \frac{1}{x+4} and \frac{\left(-x+2\right)\left(x+4\right)}{x+4} have the same denominator, add them by adding their numerators.
\frac{1-x^{2}-4x+2x+8}{x+4}
Do the multiplications in 1+\left(-x+2\right)\left(x+4\right).
\frac{9-x^{2}-2x}{x+4}
Combine like terms in 1-x^{2}-4x+2x+8.
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}