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\frac{a}{a-2}
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\frac{a}{a-2}
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\frac{2\left(a^{2}-1\right)}{\left(a-1\right)\left(2a-4\right)}+\frac{1}{2-a}
Multiply \frac{2}{a-1} times \frac{a^{2}-1}{2a-4} by multiplying numerator times numerator and denominator times denominator.
\frac{2\left(a^{2}-1\right)}{2\left(a-2\right)\left(a-1\right)}+\frac{1}{2-a}
Factor \left(a-1\right)\left(2a-4\right).
\frac{2\left(a^{2}-1\right)}{2\left(a-2\right)\left(a-1\right)}+\frac{-2\left(a-1\right)}{2\left(a-2\right)\left(a-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(a-2\right)\left(a-1\right) and 2-a is 2\left(a-2\right)\left(a-1\right). Multiply \frac{1}{2-a} times \frac{-2\left(a-1\right)}{-2\left(a-1\right)}.
\frac{2\left(a^{2}-1\right)-2\left(a-1\right)}{2\left(a-2\right)\left(a-1\right)}
Since \frac{2\left(a^{2}-1\right)}{2\left(a-2\right)\left(a-1\right)} and \frac{-2\left(a-1\right)}{2\left(a-2\right)\left(a-1\right)} have the same denominator, add them by adding their numerators.
\frac{2a^{2}-2-2a+2}{2\left(a-2\right)\left(a-1\right)}
Do the multiplications in 2\left(a^{2}-1\right)-2\left(a-1\right).
\frac{2a^{2}-2a}{2\left(a-2\right)\left(a-1\right)}
Combine like terms in 2a^{2}-2-2a+2.
\frac{2a\left(a-1\right)}{2\left(a-2\right)\left(a-1\right)}
Factor the expressions that are not already factored in \frac{2a^{2}-2a}{2\left(a-2\right)\left(a-1\right)}.
\frac{a}{a-2}
Cancel out 2\left(a-1\right) in both numerator and denominator.
\frac{2\left(a^{2}-1\right)}{\left(a-1\right)\left(2a-4\right)}+\frac{1}{2-a}
Multiply \frac{2}{a-1} times \frac{a^{2}-1}{2a-4} by multiplying numerator times numerator and denominator times denominator.
\frac{2\left(a^{2}-1\right)}{2\left(a-2\right)\left(a-1\right)}+\frac{1}{2-a}
Factor \left(a-1\right)\left(2a-4\right).
\frac{2\left(a^{2}-1\right)}{2\left(a-2\right)\left(a-1\right)}+\frac{-2\left(a-1\right)}{2\left(a-2\right)\left(a-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(a-2\right)\left(a-1\right) and 2-a is 2\left(a-2\right)\left(a-1\right). Multiply \frac{1}{2-a} times \frac{-2\left(a-1\right)}{-2\left(a-1\right)}.
\frac{2\left(a^{2}-1\right)-2\left(a-1\right)}{2\left(a-2\right)\left(a-1\right)}
Since \frac{2\left(a^{2}-1\right)}{2\left(a-2\right)\left(a-1\right)} and \frac{-2\left(a-1\right)}{2\left(a-2\right)\left(a-1\right)} have the same denominator, add them by adding their numerators.
\frac{2a^{2}-2-2a+2}{2\left(a-2\right)\left(a-1\right)}
Do the multiplications in 2\left(a^{2}-1\right)-2\left(a-1\right).
\frac{2a^{2}-2a}{2\left(a-2\right)\left(a-1\right)}
Combine like terms in 2a^{2}-2-2a+2.
\frac{2a\left(a-1\right)}{2\left(a-2\right)\left(a-1\right)}
Factor the expressions that are not already factored in \frac{2a^{2}-2a}{2\left(a-2\right)\left(a-1\right)}.
\frac{a}{a-2}
Cancel out 2\left(a-1\right) 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}