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\frac{\frac{x^{2}+4}{x}-\frac{4x}{x}}{\frac{x^{2}-4}{x^{2}+2x}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x}{x}.
\frac{\frac{x^{2}+4-4x}{x}}{\frac{x^{2}-4}{x^{2}+2x}}
Since \frac{x^{2}+4}{x} and \frac{4x}{x} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{x^{2}+4-4x}{x}}{\frac{\left(x-2\right)\left(x+2\right)}{x\left(x+2\right)}}
Factor the expressions that are not already factored in \frac{x^{2}-4}{x^{2}+2x}.
\frac{\frac{x^{2}+4-4x}{x}}{\frac{x-2}{x}}
Cancel out x+2 in both numerator and denominator.
\frac{\left(x^{2}+4-4x\right)x}{x\left(x-2\right)}
Divide \frac{x^{2}+4-4x}{x} by \frac{x-2}{x} by multiplying \frac{x^{2}+4-4x}{x} by the reciprocal of \frac{x-2}{x}.
\frac{x^{2}-4x+4}{x-2}
Cancel out x in both numerator and denominator.
\frac{\left(x-2\right)^{2}}{x-2}
Factor the expressions that are not already factored.
x-2
Cancel out x-2 in both numerator and denominator.
\frac{\frac{x^{2}+4}{x}-\frac{4x}{x}}{\frac{x^{2}-4}{x^{2}+2x}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x}{x}.
\frac{\frac{x^{2}+4-4x}{x}}{\frac{x^{2}-4}{x^{2}+2x}}
Since \frac{x^{2}+4}{x} and \frac{4x}{x} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{x^{2}+4-4x}{x}}{\frac{\left(x-2\right)\left(x+2\right)}{x\left(x+2\right)}}
Factor the expressions that are not already factored in \frac{x^{2}-4}{x^{2}+2x}.
\frac{\frac{x^{2}+4-4x}{x}}{\frac{x-2}{x}}
Cancel out x+2 in both numerator and denominator.
\frac{\left(x^{2}+4-4x\right)x}{x\left(x-2\right)}
Divide \frac{x^{2}+4-4x}{x} by \frac{x-2}{x} by multiplying \frac{x^{2}+4-4x}{x} by the reciprocal of \frac{x-2}{x}.
\frac{x^{2}-4x+4}{x-2}
Cancel out x in both numerator and denominator.
\frac{\left(x-2\right)^{2}}{x-2}
Factor the expressions that are not already factored.
x-2
Cancel out x-2 in both numerator and denominator.
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}