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