Evaluate
\frac{x^{2}-2x+4}{x^{2}-4}
Expand
\frac{x^{2}-2x+4}{x^{2}-4}
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\frac{\left(x+2\right)\left(x^{3}+8\right)}{\left(x^{2}+4x+4\right)\left(x^{2}-4\right)}
Divide \frac{x+2}{x^{2}+4x+4} by \frac{x^{2}-4}{x^{3}+8} by multiplying \frac{x+2}{x^{2}+4x+4} by the reciprocal of \frac{x^{2}-4}{x^{3}+8}.
\frac{\left(x+2\right)^{2}\left(x^{2}-2x+4\right)}{\left(x-2\right)\left(x+2\right)\left(x+2\right)^{2}}
Factor the expressions that are not already factored.
\frac{x^{2}-2x+4}{\left(x-2\right)\left(x+2\right)}
Cancel out \left(x+2\right)\left(x+2\right) in both numerator and denominator.
\frac{x^{2}-2x+4}{x^{2}-4}
Expand the expression.
\frac{\left(x+2\right)\left(x^{3}+8\right)}{\left(x^{2}+4x+4\right)\left(x^{2}-4\right)}
Divide \frac{x+2}{x^{2}+4x+4} by \frac{x^{2}-4}{x^{3}+8} by multiplying \frac{x+2}{x^{2}+4x+4} by the reciprocal of \frac{x^{2}-4}{x^{3}+8}.
\frac{\left(x+2\right)^{2}\left(x^{2}-2x+4\right)}{\left(x-2\right)\left(x+2\right)\left(x+2\right)^{2}}
Factor the expressions that are not already factored.
\frac{x^{2}-2x+4}{\left(x-2\right)\left(x+2\right)}
Cancel out \left(x+2\right)\left(x+2\right) in both numerator and denominator.
\frac{x^{2}-2x+4}{x^{2}-4}
Expand the expression.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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Matrix
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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}