Evaluate
-\frac{2}{\left(A-1\right)\left(A+B-1\right)}
Expand
-\frac{2}{\left(A-1\right)\left(A+B-1\right)}
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\frac{A+B+1}{B\left(A+B-1\right)}-\frac{A+1}{B\left(A-1\right)}
Factor B^{2}+AB-B. Factor AB-B.
\frac{\left(A+B+1\right)\left(A-1\right)}{B\left(A-1\right)\left(A+B-1\right)}-\frac{\left(A+1\right)\left(A+B-1\right)}{B\left(A-1\right)\left(A+B-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of B\left(A+B-1\right) and B\left(A-1\right) is B\left(A-1\right)\left(A+B-1\right). Multiply \frac{A+B+1}{B\left(A+B-1\right)} times \frac{A-1}{A-1}. Multiply \frac{A+1}{B\left(A-1\right)} times \frac{A+B-1}{A+B-1}.
\frac{\left(A+B+1\right)\left(A-1\right)-\left(A+1\right)\left(A+B-1\right)}{B\left(A-1\right)\left(A+B-1\right)}
Since \frac{\left(A+B+1\right)\left(A-1\right)}{B\left(A-1\right)\left(A+B-1\right)} and \frac{\left(A+1\right)\left(A+B-1\right)}{B\left(A-1\right)\left(A+B-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{A^{2}-A+AB-B+A-1-A^{2}-AB+A-A-B+1}{B\left(A-1\right)\left(A+B-1\right)}
Do the multiplications in \left(A+B+1\right)\left(A-1\right)-\left(A+1\right)\left(A+B-1\right).
\frac{-2B}{B\left(A-1\right)\left(A+B-1\right)}
Combine like terms in A^{2}-A+AB-B+A-1-A^{2}-AB+A-A-B+1.
\frac{-2}{\left(A-1\right)\left(A+B-1\right)}
Cancel out B in both numerator and denominator.
\frac{-2}{A^{2}+AB-2A-B+1}
Expand \left(A-1\right)\left(A+B-1\right).
\frac{A+B+1}{B\left(A+B-1\right)}-\frac{A+1}{B\left(A-1\right)}
Factor B^{2}+AB-B. Factor AB-B.
\frac{\left(A+B+1\right)\left(A-1\right)}{B\left(A-1\right)\left(A+B-1\right)}-\frac{\left(A+1\right)\left(A+B-1\right)}{B\left(A-1\right)\left(A+B-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of B\left(A+B-1\right) and B\left(A-1\right) is B\left(A-1\right)\left(A+B-1\right). Multiply \frac{A+B+1}{B\left(A+B-1\right)} times \frac{A-1}{A-1}. Multiply \frac{A+1}{B\left(A-1\right)} times \frac{A+B-1}{A+B-1}.
\frac{\left(A+B+1\right)\left(A-1\right)-\left(A+1\right)\left(A+B-1\right)}{B\left(A-1\right)\left(A+B-1\right)}
Since \frac{\left(A+B+1\right)\left(A-1\right)}{B\left(A-1\right)\left(A+B-1\right)} and \frac{\left(A+1\right)\left(A+B-1\right)}{B\left(A-1\right)\left(A+B-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{A^{2}-A+AB-B+A-1-A^{2}-AB+A-A-B+1}{B\left(A-1\right)\left(A+B-1\right)}
Do the multiplications in \left(A+B+1\right)\left(A-1\right)-\left(A+1\right)\left(A+B-1\right).
\frac{-2B}{B\left(A-1\right)\left(A+B-1\right)}
Combine like terms in A^{2}-A+AB-B+A-1-A^{2}-AB+A-A-B+1.
\frac{-2}{\left(A-1\right)\left(A+B-1\right)}
Cancel out B in both numerator and denominator.
\frac{-2}{A^{2}+AB-2A-B+1}
Expand \left(A-1\right)\left(A+B-1\right).
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}