Evaluate
\frac{6}{\left(x+1\right)\left(x+4\right)}
Expand
\frac{6}{\left(x+1\right)\left(x+4\right)}
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\frac{6}{x+4}-\frac{2\times 3x}{\left(x+1\right)\left(x+4\right)}
Divide \frac{2}{x+1} by \frac{x+4}{3x} by multiplying \frac{2}{x+1} by the reciprocal of \frac{x+4}{3x}.
\frac{6}{x+4}-\frac{6x}{\left(x+1\right)\left(x+4\right)}
Multiply 2 and 3 to get 6.
\frac{6\left(x+1\right)}{\left(x+1\right)\left(x+4\right)}-\frac{6x}{\left(x+1\right)\left(x+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+4 and \left(x+1\right)\left(x+4\right) is \left(x+1\right)\left(x+4\right). Multiply \frac{6}{x+4} times \frac{x+1}{x+1}.
\frac{6\left(x+1\right)-6x}{\left(x+1\right)\left(x+4\right)}
Since \frac{6\left(x+1\right)}{\left(x+1\right)\left(x+4\right)} and \frac{6x}{\left(x+1\right)\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{6x+6-6x}{\left(x+1\right)\left(x+4\right)}
Do the multiplications in 6\left(x+1\right)-6x.
\frac{6}{\left(x+1\right)\left(x+4\right)}
Combine like terms in 6x+6-6x.
\frac{6}{x^{2}+5x+4}
Expand \left(x+1\right)\left(x+4\right).
\frac{6}{x+4}-\frac{2\times 3x}{\left(x+1\right)\left(x+4\right)}
Divide \frac{2}{x+1} by \frac{x+4}{3x} by multiplying \frac{2}{x+1} by the reciprocal of \frac{x+4}{3x}.
\frac{6}{x+4}-\frac{6x}{\left(x+1\right)\left(x+4\right)}
Multiply 2 and 3 to get 6.
\frac{6\left(x+1\right)}{\left(x+1\right)\left(x+4\right)}-\frac{6x}{\left(x+1\right)\left(x+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+4 and \left(x+1\right)\left(x+4\right) is \left(x+1\right)\left(x+4\right). Multiply \frac{6}{x+4} times \frac{x+1}{x+1}.
\frac{6\left(x+1\right)-6x}{\left(x+1\right)\left(x+4\right)}
Since \frac{6\left(x+1\right)}{\left(x+1\right)\left(x+4\right)} and \frac{6x}{\left(x+1\right)\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{6x+6-6x}{\left(x+1\right)\left(x+4\right)}
Do the multiplications in 6\left(x+1\right)-6x.
\frac{6}{\left(x+1\right)\left(x+4\right)}
Combine like terms in 6x+6-6x.
\frac{6}{x^{2}+5x+4}
Expand \left(x+1\right)\left(x+4\right).
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
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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}