Evaluate
\frac{1}{2}=0.5
Factor
\frac{1}{2} = 0.5
Graph
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\frac{\frac{\left(x+3\right)\left(x-4\right)}{\left(x-4\right)\left(x+4\right)}-\frac{\left(x-3\right)\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}}{\frac{4x}{16-x^{2}}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+4 and x-4 is \left(x-4\right)\left(x+4\right). Multiply \frac{x+3}{x+4} times \frac{x-4}{x-4}. Multiply \frac{x-3}{x-4} times \frac{x+4}{x+4}.
\frac{\frac{\left(x+3\right)\left(x-4\right)-\left(x-3\right)\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}}{\frac{4x}{16-x^{2}}}
Since \frac{\left(x+3\right)\left(x-4\right)}{\left(x-4\right)\left(x+4\right)} and \frac{\left(x-3\right)\left(x+4\right)}{\left(x-4\right)\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{x^{2}-4x+3x-12-x^{2}-4x+3x+12}{\left(x-4\right)\left(x+4\right)}}{\frac{4x}{16-x^{2}}}
Do the multiplications in \left(x+3\right)\left(x-4\right)-\left(x-3\right)\left(x+4\right).
\frac{\frac{-2x}{\left(x-4\right)\left(x+4\right)}}{\frac{4x}{16-x^{2}}}
Combine like terms in x^{2}-4x+3x-12-x^{2}-4x+3x+12.
\frac{-2x\left(16-x^{2}\right)}{\left(x-4\right)\left(x+4\right)\times 4x}
Divide \frac{-2x}{\left(x-4\right)\left(x+4\right)} by \frac{4x}{16-x^{2}} by multiplying \frac{-2x}{\left(x-4\right)\left(x+4\right)} by the reciprocal of \frac{4x}{16-x^{2}}.
\frac{-\left(-x^{2}+16\right)}{2\left(x-4\right)\left(x+4\right)}
Cancel out 2x in both numerator and denominator.
\frac{-\left(x-4\right)\left(-x-4\right)}{2\left(x-4\right)\left(x+4\right)}
Factor the expressions that are not already factored.
\frac{-\left(-1\right)\left(x-4\right)\left(x+4\right)}{2\left(x-4\right)\left(x+4\right)}
Extract the negative sign in -4-x.
\frac{-\left(-1\right)}{2}
Cancel out \left(x-4\right)\left(x+4\right) in both numerator and denominator.
\frac{1}{2}
Multiply -1 and -1 to get 1.
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}