Evaluate
\frac{8c}{\left(b-1\right)\left(b+3\right)}
Expand
\frac{8c}{\left(b-1\right)\left(b+3\right)}
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\frac{2c}{b-1}+\frac{-2c\left(b-1\right)}{\left(b-1\right)\left(b+3\right)}
Cancel out b+3 in both numerator and denominator.
\frac{2c}{b-1}+\frac{-2c}{b+3}
Cancel out b-1 in both numerator and denominator.
\frac{2c\left(b+3\right)}{\left(b-1\right)\left(b+3\right)}+\frac{-2c\left(b-1\right)}{\left(b-1\right)\left(b+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b-1 and b+3 is \left(b-1\right)\left(b+3\right). Multiply \frac{2c}{b-1} times \frac{b+3}{b+3}. Multiply \frac{-2c}{b+3} times \frac{b-1}{b-1}.
\frac{2c\left(b+3\right)-2c\left(b-1\right)}{\left(b-1\right)\left(b+3\right)}
Since \frac{2c\left(b+3\right)}{\left(b-1\right)\left(b+3\right)} and \frac{-2c\left(b-1\right)}{\left(b-1\right)\left(b+3\right)} have the same denominator, add them by adding their numerators.
\frac{2cb+6c-2cb+2c}{\left(b-1\right)\left(b+3\right)}
Do the multiplications in 2c\left(b+3\right)-2c\left(b-1\right).
\frac{8c}{\left(b-1\right)\left(b+3\right)}
Combine like terms in 2cb+6c-2cb+2c.
\frac{8c}{b^{2}+2b-3}
Expand \left(b-1\right)\left(b+3\right).
\frac{2c}{b-1}+\frac{-2c\left(b-1\right)}{\left(b-1\right)\left(b+3\right)}
Cancel out b+3 in both numerator and denominator.
\frac{2c}{b-1}+\frac{-2c}{b+3}
Cancel out b-1 in both numerator and denominator.
\frac{2c\left(b+3\right)}{\left(b-1\right)\left(b+3\right)}+\frac{-2c\left(b-1\right)}{\left(b-1\right)\left(b+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b-1 and b+3 is \left(b-1\right)\left(b+3\right). Multiply \frac{2c}{b-1} times \frac{b+3}{b+3}. Multiply \frac{-2c}{b+3} times \frac{b-1}{b-1}.
\frac{2c\left(b+3\right)-2c\left(b-1\right)}{\left(b-1\right)\left(b+3\right)}
Since \frac{2c\left(b+3\right)}{\left(b-1\right)\left(b+3\right)} and \frac{-2c\left(b-1\right)}{\left(b-1\right)\left(b+3\right)} have the same denominator, add them by adding their numerators.
\frac{2cb+6c-2cb+2c}{\left(b-1\right)\left(b+3\right)}
Do the multiplications in 2c\left(b+3\right)-2c\left(b-1\right).
\frac{8c}{\left(b-1\right)\left(b+3\right)}
Combine like terms in 2cb+6c-2cb+2c.
\frac{8c}{b^{2}+2b-3}
Expand \left(b-1\right)\left(b+3\right).
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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
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