Evaluate
-\frac{2}{\left(a-1\right)\left(x-1\right)}
Expand
-\frac{2}{\left(a-1\right)\left(x-1\right)}
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\frac{\frac{\left(x+1\right)\left(a-1\right)}{\left(a-1\right)\left(x-1\right)}-\frac{\left(a+1\right)\left(x-1\right)}{\left(a-1\right)\left(x-1\right)}}{x-a}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and a-1 is \left(a-1\right)\left(x-1\right). Multiply \frac{x+1}{x-1} times \frac{a-1}{a-1}. Multiply \frac{a+1}{a-1} times \frac{x-1}{x-1}.
\frac{\frac{\left(x+1\right)\left(a-1\right)-\left(a+1\right)\left(x-1\right)}{\left(a-1\right)\left(x-1\right)}}{x-a}
Since \frac{\left(x+1\right)\left(a-1\right)}{\left(a-1\right)\left(x-1\right)} and \frac{\left(a+1\right)\left(x-1\right)}{\left(a-1\right)\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{xa-x+a-1-ax+a-x+1}{\left(a-1\right)\left(x-1\right)}}{x-a}
Do the multiplications in \left(x+1\right)\left(a-1\right)-\left(a+1\right)\left(x-1\right).
\frac{\frac{-2x+2a}{\left(a-1\right)\left(x-1\right)}}{x-a}
Combine like terms in xa-x+a-1-ax+a-x+1.
\frac{-2x+2a}{\left(a-1\right)\left(x-1\right)\left(x-a\right)}
Express \frac{\frac{-2x+2a}{\left(a-1\right)\left(x-1\right)}}{x-a} as a single fraction.
\frac{2\left(-x+a\right)}{\left(a-1\right)\left(x-1\right)\left(x-a\right)}
Factor the expressions that are not already factored.
\frac{-2\left(x-a\right)}{\left(a-1\right)\left(x-1\right)\left(x-a\right)}
Extract the negative sign in -x+a.
\frac{-2}{\left(a-1\right)\left(x-1\right)}
Cancel out x-a in both numerator and denominator.
\frac{-2}{ax-x-a+1}
Expand the expression.
\frac{\frac{\left(x+1\right)\left(a-1\right)}{\left(a-1\right)\left(x-1\right)}-\frac{\left(a+1\right)\left(x-1\right)}{\left(a-1\right)\left(x-1\right)}}{x-a}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and a-1 is \left(a-1\right)\left(x-1\right). Multiply \frac{x+1}{x-1} times \frac{a-1}{a-1}. Multiply \frac{a+1}{a-1} times \frac{x-1}{x-1}.
\frac{\frac{\left(x+1\right)\left(a-1\right)-\left(a+1\right)\left(x-1\right)}{\left(a-1\right)\left(x-1\right)}}{x-a}
Since \frac{\left(x+1\right)\left(a-1\right)}{\left(a-1\right)\left(x-1\right)} and \frac{\left(a+1\right)\left(x-1\right)}{\left(a-1\right)\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{xa-x+a-1-ax+a-x+1}{\left(a-1\right)\left(x-1\right)}}{x-a}
Do the multiplications in \left(x+1\right)\left(a-1\right)-\left(a+1\right)\left(x-1\right).
\frac{\frac{-2x+2a}{\left(a-1\right)\left(x-1\right)}}{x-a}
Combine like terms in xa-x+a-1-ax+a-x+1.
\frac{-2x+2a}{\left(a-1\right)\left(x-1\right)\left(x-a\right)}
Express \frac{\frac{-2x+2a}{\left(a-1\right)\left(x-1\right)}}{x-a} as a single fraction.
\frac{2\left(-x+a\right)}{\left(a-1\right)\left(x-1\right)\left(x-a\right)}
Factor the expressions that are not already factored.
\frac{-2\left(x-a\right)}{\left(a-1\right)\left(x-1\right)\left(x-a\right)}
Extract the negative sign in -x+a.
\frac{-2}{\left(a-1\right)\left(x-1\right)}
Cancel out x-a in both numerator and denominator.
\frac{-2}{ax-x-a+1}
Expand the expression.
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}