Evaluate
\frac{5x+7}{\left(x+1\right)\left(x+2\right)\left(x+4\right)}
Expand
\frac{5x+7}{\left(x+1\right)\left(x+2\right)\left(x+4\right)}
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\frac{3\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+4\right)}+\frac{2\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+2\right)\left(x+4\right) and \left(x+1\right)\left(x+4\right) is \left(x+1\right)\left(x+2\right)\left(x+4\right). Multiply \frac{3}{\left(x+2\right)\left(x+4\right)} times \frac{x+1}{x+1}. Multiply \frac{2}{\left(x+1\right)\left(x+4\right)} times \frac{x+2}{x+2}.
\frac{3\left(x+1\right)+2\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x+4\right)}
Since \frac{3\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+4\right)} and \frac{2\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x+4\right)} have the same denominator, add them by adding their numerators.
\frac{3x+3+2x+4}{\left(x+1\right)\left(x+2\right)\left(x+4\right)}
Do the multiplications in 3\left(x+1\right)+2\left(x+2\right).
\frac{5x+7}{\left(x+1\right)\left(x+2\right)\left(x+4\right)}
Combine like terms in 3x+3+2x+4.
\frac{5x+7}{x^{3}+7x^{2}+14x+8}
Expand \left(x+1\right)\left(x+2\right)\left(x+4\right).
\frac{3\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+4\right)}+\frac{2\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+2\right)\left(x+4\right) and \left(x+1\right)\left(x+4\right) is \left(x+1\right)\left(x+2\right)\left(x+4\right). Multiply \frac{3}{\left(x+2\right)\left(x+4\right)} times \frac{x+1}{x+1}. Multiply \frac{2}{\left(x+1\right)\left(x+4\right)} times \frac{x+2}{x+2}.
\frac{3\left(x+1\right)+2\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x+4\right)}
Since \frac{3\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+4\right)} and \frac{2\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x+4\right)} have the same denominator, add them by adding their numerators.
\frac{3x+3+2x+4}{\left(x+1\right)\left(x+2\right)\left(x+4\right)}
Do the multiplications in 3\left(x+1\right)+2\left(x+2\right).
\frac{5x+7}{\left(x+1\right)\left(x+2\right)\left(x+4\right)}
Combine like terms in 3x+3+2x+4.
\frac{5x+7}{x^{3}+7x^{2}+14x+8}
Expand \left(x+1\right)\left(x+2\right)\left(x+4\right).
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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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