\frac { \frac { 1 } { x + a + b } - \frac { 1 } { x - a + b } } { \frac { 1 } { x - a + b } - \frac { 1 } { x + a + b } } d e
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\frac{\frac{x+b-a}{\left(x+a+b\right)\left(x+b-a\right)}-\frac{x+a+b}{\left(x+a+b\right)\left(x+b-a\right)}}{\frac{1}{x-a+b}-\frac{1}{x+a+b}}de
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+a+b and x-a+b is \left(x+a+b\right)\left(x+b-a\right). Multiply \frac{1}{x+a+b} times \frac{x+b-a}{x+b-a}. Multiply \frac{1}{x-a+b} times \frac{x+a+b}{x+a+b}.
\frac{\frac{x+b-a-\left(x+a+b\right)}{\left(x+a+b\right)\left(x+b-a\right)}}{\frac{1}{x-a+b}-\frac{1}{x+a+b}}de
Since \frac{x+b-a}{\left(x+a+b\right)\left(x+b-a\right)} and \frac{x+a+b}{\left(x+a+b\right)\left(x+b-a\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{x+b-a-x-a-b}{\left(x+a+b\right)\left(x+b-a\right)}}{\frac{1}{x-a+b}-\frac{1}{x+a+b}}de
Do the multiplications in x+b-a-\left(x+a+b\right).
\frac{\frac{-2a}{\left(x+a+b\right)\left(x+b-a\right)}}{\frac{1}{x-a+b}-\frac{1}{x+a+b}}de
Combine like terms in x+b-a-x-a-b.
\frac{\frac{-2a}{\left(x+a+b\right)\left(x+b-a\right)}}{\frac{x+a+b}{\left(x+a+b\right)\left(x+b-a\right)}-\frac{x+b-a}{\left(x+a+b\right)\left(x+b-a\right)}}de
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-a+b and x+a+b is \left(x+a+b\right)\left(x+b-a\right). Multiply \frac{1}{x-a+b} times \frac{x+a+b}{x+a+b}. Multiply \frac{1}{x+a+b} times \frac{x+b-a}{x+b-a}.
\frac{\frac{-2a}{\left(x+a+b\right)\left(x+b-a\right)}}{\frac{x+a+b-\left(x+b-a\right)}{\left(x+a+b\right)\left(x+b-a\right)}}de
Since \frac{x+a+b}{\left(x+a+b\right)\left(x+b-a\right)} and \frac{x+b-a}{\left(x+a+b\right)\left(x+b-a\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{-2a}{\left(x+a+b\right)\left(x+b-a\right)}}{\frac{x+a+b-x-b+a}{\left(x+a+b\right)\left(x+b-a\right)}}de
Do the multiplications in x+a+b-\left(x+b-a\right).
\frac{\frac{-2a}{\left(x+a+b\right)\left(x+b-a\right)}}{\frac{2a}{\left(x+a+b\right)\left(x+b-a\right)}}de
Combine like terms in x+a+b-x-b+a.
\frac{-2a\left(x+a+b\right)\left(x+b-a\right)}{\left(x+a+b\right)\left(x+b-a\right)\times 2a}de
Divide \frac{-2a}{\left(x+a+b\right)\left(x+b-a\right)} by \frac{2a}{\left(x+a+b\right)\left(x+b-a\right)} by multiplying \frac{-2a}{\left(x+a+b\right)\left(x+b-a\right)} by the reciprocal of \frac{2a}{\left(x+a+b\right)\left(x+b-a\right)}.
-de
Cancel out 2a\left(x+a+b\right)\left(x+b-a\right) in both numerator and denominator.
\frac{\frac{x+b-a}{\left(x+a+b\right)\left(x+b-a\right)}-\frac{x+a+b}{\left(x+a+b\right)\left(x+b-a\right)}}{\frac{1}{x-a+b}-\frac{1}{x+a+b}}de
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+a+b and x-a+b is \left(x+a+b\right)\left(x+b-a\right). Multiply \frac{1}{x+a+b} times \frac{x+b-a}{x+b-a}. Multiply \frac{1}{x-a+b} times \frac{x+a+b}{x+a+b}.
\frac{\frac{x+b-a-\left(x+a+b\right)}{\left(x+a+b\right)\left(x+b-a\right)}}{\frac{1}{x-a+b}-\frac{1}{x+a+b}}de
Since \frac{x+b-a}{\left(x+a+b\right)\left(x+b-a\right)} and \frac{x+a+b}{\left(x+a+b\right)\left(x+b-a\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{x+b-a-x-a-b}{\left(x+a+b\right)\left(x+b-a\right)}}{\frac{1}{x-a+b}-\frac{1}{x+a+b}}de
Do the multiplications in x+b-a-\left(x+a+b\right).
\frac{\frac{-2a}{\left(x+a+b\right)\left(x+b-a\right)}}{\frac{1}{x-a+b}-\frac{1}{x+a+b}}de
Combine like terms in x+b-a-x-a-b.
\frac{\frac{-2a}{\left(x+a+b\right)\left(x+b-a\right)}}{\frac{x+a+b}{\left(x+a+b\right)\left(x+b-a\right)}-\frac{x+b-a}{\left(x+a+b\right)\left(x+b-a\right)}}de
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-a+b and x+a+b is \left(x+a+b\right)\left(x+b-a\right). Multiply \frac{1}{x-a+b} times \frac{x+a+b}{x+a+b}. Multiply \frac{1}{x+a+b} times \frac{x+b-a}{x+b-a}.
\frac{\frac{-2a}{\left(x+a+b\right)\left(x+b-a\right)}}{\frac{x+a+b-\left(x+b-a\right)}{\left(x+a+b\right)\left(x+b-a\right)}}de
Since \frac{x+a+b}{\left(x+a+b\right)\left(x+b-a\right)} and \frac{x+b-a}{\left(x+a+b\right)\left(x+b-a\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{-2a}{\left(x+a+b\right)\left(x+b-a\right)}}{\frac{x+a+b-x-b+a}{\left(x+a+b\right)\left(x+b-a\right)}}de
Do the multiplications in x+a+b-\left(x+b-a\right).
\frac{\frac{-2a}{\left(x+a+b\right)\left(x+b-a\right)}}{\frac{2a}{\left(x+a+b\right)\left(x+b-a\right)}}de
Combine like terms in x+a+b-x-b+a.
\frac{-2a\left(x+a+b\right)\left(x+b-a\right)}{\left(x+a+b\right)\left(x+b-a\right)\times 2a}de
Divide \frac{-2a}{\left(x+a+b\right)\left(x+b-a\right)} by \frac{2a}{\left(x+a+b\right)\left(x+b-a\right)} by multiplying \frac{-2a}{\left(x+a+b\right)\left(x+b-a\right)} by the reciprocal of \frac{2a}{\left(x+a+b\right)\left(x+b-a\right)}.
-de
Cancel out 2a\left(x+a+b\right)\left(x+b-a\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}