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\frac{2}{x+1}
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\frac{2}{x+1}
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\frac{2x}{x+1}-\frac{\left(2x-4\right)\left(x^{2}-2x+1\right)}{\left(x^{2}-1\right)\left(x-2\right)}
Divide \frac{2x-4}{x^{2}-1} by \frac{x-2}{x^{2}-2x+1} by multiplying \frac{2x-4}{x^{2}-1} by the reciprocal of \frac{x-2}{x^{2}-2x+1}.
\frac{2x}{x+1}-\frac{2\left(x-2\right)\left(x-1\right)^{2}}{\left(x-2\right)\left(x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored in \frac{\left(2x-4\right)\left(x^{2}-2x+1\right)}{\left(x^{2}-1\right)\left(x-2\right)}.
\frac{2x}{x+1}-\frac{2\left(x-1\right)}{x+1}
Cancel out \left(x-2\right)\left(x-1\right) in both numerator and denominator.
\frac{2x-2\left(x-1\right)}{x+1}
Since \frac{2x}{x+1} and \frac{2\left(x-1\right)}{x+1} have the same denominator, subtract them by subtracting their numerators.
\frac{2x-2x+2}{x+1}
Do the multiplications in 2x-2\left(x-1\right).
\frac{2}{x+1}
Combine like terms in 2x-2x+2.
\frac{2x}{x+1}-\frac{\left(2x-4\right)\left(x^{2}-2x+1\right)}{\left(x^{2}-1\right)\left(x-2\right)}
Divide \frac{2x-4}{x^{2}-1} by \frac{x-2}{x^{2}-2x+1} by multiplying \frac{2x-4}{x^{2}-1} by the reciprocal of \frac{x-2}{x^{2}-2x+1}.
\frac{2x}{x+1}-\frac{2\left(x-2\right)\left(x-1\right)^{2}}{\left(x-2\right)\left(x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored in \frac{\left(2x-4\right)\left(x^{2}-2x+1\right)}{\left(x^{2}-1\right)\left(x-2\right)}.
\frac{2x}{x+1}-\frac{2\left(x-1\right)}{x+1}
Cancel out \left(x-2\right)\left(x-1\right) in both numerator and denominator.
\frac{2x-2\left(x-1\right)}{x+1}
Since \frac{2x}{x+1} and \frac{2\left(x-1\right)}{x+1} have the same denominator, subtract them by subtracting their numerators.
\frac{2x-2x+2}{x+1}
Do the multiplications in 2x-2\left(x-1\right).
\frac{2}{x+1}
Combine like terms in 2x-2x+2.
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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
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