Evaluate
\frac{16+9x-x^{2}}{\left(x-4\right)\left(x^{2}-4\right)}
Expand
\frac{16+9x-x^{2}}{\left(x-4\right)\left(x^{2}-4\right)}
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\frac{x+3}{\left(x-2\right)\left(x+2\right)}-\frac{5}{x-2}+\frac{3}{x-4}
Factor x^{2}-4.
\frac{x+3}{\left(x-2\right)\left(x+2\right)}-\frac{5\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{3}{x-4}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-2\right)\left(x+2\right) and x-2 is \left(x-2\right)\left(x+2\right). Multiply \frac{5}{x-2} times \frac{x+2}{x+2}.
\frac{x+3-5\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{3}{x-4}
Since \frac{x+3}{\left(x-2\right)\left(x+2\right)} and \frac{5\left(x+2\right)}{\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x+3-5x-10}{\left(x-2\right)\left(x+2\right)}+\frac{3}{x-4}
Do the multiplications in x+3-5\left(x+2\right).
\frac{-4x-7}{\left(x-2\right)\left(x+2\right)}+\frac{3}{x-4}
Combine like terms in x+3-5x-10.
\frac{\left(-4x-7\right)\left(x-4\right)}{\left(x-4\right)\left(x-2\right)\left(x+2\right)}+\frac{3\left(x-2\right)\left(x+2\right)}{\left(x-4\right)\left(x-2\right)\left(x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-2\right)\left(x+2\right) and x-4 is \left(x-4\right)\left(x-2\right)\left(x+2\right). Multiply \frac{-4x-7}{\left(x-2\right)\left(x+2\right)} times \frac{x-4}{x-4}. Multiply \frac{3}{x-4} times \frac{\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}.
\frac{\left(-4x-7\right)\left(x-4\right)+3\left(x-2\right)\left(x+2\right)}{\left(x-4\right)\left(x-2\right)\left(x+2\right)}
Since \frac{\left(-4x-7\right)\left(x-4\right)}{\left(x-4\right)\left(x-2\right)\left(x+2\right)} and \frac{3\left(x-2\right)\left(x+2\right)}{\left(x-4\right)\left(x-2\right)\left(x+2\right)} have the same denominator, add them by adding their numerators.
\frac{-4x^{2}+16x-7x+28+3x^{2}+6x-6x-12}{\left(x-4\right)\left(x-2\right)\left(x+2\right)}
Do the multiplications in \left(-4x-7\right)\left(x-4\right)+3\left(x-2\right)\left(x+2\right).
\frac{-x^{2}+9x+16}{\left(x-4\right)\left(x-2\right)\left(x+2\right)}
Combine like terms in -4x^{2}+16x-7x+28+3x^{2}+6x-6x-12.
\frac{-x^{2}+9x+16}{x^{3}-4x^{2}-4x+16}
Expand \left(x-4\right)\left(x-2\right)\left(x+2\right).
\frac{x+3}{\left(x-2\right)\left(x+2\right)}-\frac{5}{x-2}+\frac{3}{x-4}
Factor x^{2}-4.
\frac{x+3}{\left(x-2\right)\left(x+2\right)}-\frac{5\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{3}{x-4}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-2\right)\left(x+2\right) and x-2 is \left(x-2\right)\left(x+2\right). Multiply \frac{5}{x-2} times \frac{x+2}{x+2}.
\frac{x+3-5\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{3}{x-4}
Since \frac{x+3}{\left(x-2\right)\left(x+2\right)} and \frac{5\left(x+2\right)}{\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x+3-5x-10}{\left(x-2\right)\left(x+2\right)}+\frac{3}{x-4}
Do the multiplications in x+3-5\left(x+2\right).
\frac{-4x-7}{\left(x-2\right)\left(x+2\right)}+\frac{3}{x-4}
Combine like terms in x+3-5x-10.
\frac{\left(-4x-7\right)\left(x-4\right)}{\left(x-4\right)\left(x-2\right)\left(x+2\right)}+\frac{3\left(x-2\right)\left(x+2\right)}{\left(x-4\right)\left(x-2\right)\left(x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-2\right)\left(x+2\right) and x-4 is \left(x-4\right)\left(x-2\right)\left(x+2\right). Multiply \frac{-4x-7}{\left(x-2\right)\left(x+2\right)} times \frac{x-4}{x-4}. Multiply \frac{3}{x-4} times \frac{\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}.
\frac{\left(-4x-7\right)\left(x-4\right)+3\left(x-2\right)\left(x+2\right)}{\left(x-4\right)\left(x-2\right)\left(x+2\right)}
Since \frac{\left(-4x-7\right)\left(x-4\right)}{\left(x-4\right)\left(x-2\right)\left(x+2\right)} and \frac{3\left(x-2\right)\left(x+2\right)}{\left(x-4\right)\left(x-2\right)\left(x+2\right)} have the same denominator, add them by adding their numerators.
\frac{-4x^{2}+16x-7x+28+3x^{2}+6x-6x-12}{\left(x-4\right)\left(x-2\right)\left(x+2\right)}
Do the multiplications in \left(-4x-7\right)\left(x-4\right)+3\left(x-2\right)\left(x+2\right).
\frac{-x^{2}+9x+16}{\left(x-4\right)\left(x-2\right)\left(x+2\right)}
Combine like terms in -4x^{2}+16x-7x+28+3x^{2}+6x-6x-12.
\frac{-x^{2}+9x+16}{x^{3}-4x^{2}-4x+16}
Expand \left(x-4\right)\left(x-2\right)\left(x+2\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}