Evaluate
\frac{6}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}
Expand
\frac{6}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}
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\frac{3\left(x+3\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}-\frac{3\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+1\right)\left(x+2\right) and \left(x+2\right)\left(x+3\right) is \left(x+1\right)\left(x+2\right)\left(x+3\right). Multiply \frac{3}{\left(x+1\right)\left(x+2\right)} times \frac{x+3}{x+3}. Multiply \frac{3}{\left(x+2\right)\left(x+3\right)} times \frac{x+1}{x+1}.
\frac{3\left(x+3\right)-3\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}
Since \frac{3\left(x+3\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)} and \frac{3\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x+9-3x-3}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}
Do the multiplications in 3\left(x+3\right)-3\left(x+1\right).
\frac{6}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}
Combine like terms in 3x+9-3x-3.
\frac{6}{x^{3}+6x^{2}+11x+6}
Expand \left(x+1\right)\left(x+2\right)\left(x+3\right).
\frac{3\left(x+3\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}-\frac{3\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+1\right)\left(x+2\right) and \left(x+2\right)\left(x+3\right) is \left(x+1\right)\left(x+2\right)\left(x+3\right). Multiply \frac{3}{\left(x+1\right)\left(x+2\right)} times \frac{x+3}{x+3}. Multiply \frac{3}{\left(x+2\right)\left(x+3\right)} times \frac{x+1}{x+1}.
\frac{3\left(x+3\right)-3\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}
Since \frac{3\left(x+3\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)} and \frac{3\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x+9-3x-3}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}
Do the multiplications in 3\left(x+3\right)-3\left(x+1\right).
\frac{6}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}
Combine like terms in 3x+9-3x-3.
\frac{6}{x^{3}+6x^{2}+11x+6}
Expand \left(x+1\right)\left(x+2\right)\left(x+3\right).
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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699 * 533
Matrix
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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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}