Evaluate
\frac{6x^{2}+13x+10}{\left(x+1\right)\left(x+4\right)}
Expand
\frac{6x^{2}+13x+10}{\left(x+1\right)\left(x+4\right)}
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\frac{\left(x+2\right)\left(x+4\right)}{\left(x+1\right)\left(x+4\right)}+\frac{\left(5x+2\right)\left(x+1\right)}{\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+1 and x+4 is \left(x+1\right)\left(x+4\right). Multiply \frac{x+2}{x+1} times \frac{x+4}{x+4}. Multiply \frac{5x+2}{x+4} times \frac{x+1}{x+1}.
\frac{\left(x+2\right)\left(x+4\right)+\left(5x+2\right)\left(x+1\right)}{\left(x+1\right)\left(x+4\right)}
Since \frac{\left(x+2\right)\left(x+4\right)}{\left(x+1\right)\left(x+4\right)} and \frac{\left(5x+2\right)\left(x+1\right)}{\left(x+1\right)\left(x+4\right)} have the same denominator, add them by adding their numerators.
\frac{x^{2}+4x+2x+8+5x^{2}+5x+2x+2}{\left(x+1\right)\left(x+4\right)}
Do the multiplications in \left(x+2\right)\left(x+4\right)+\left(5x+2\right)\left(x+1\right).
\frac{6x^{2}+13x+10}{\left(x+1\right)\left(x+4\right)}
Combine like terms in x^{2}+4x+2x+8+5x^{2}+5x+2x+2.
\frac{6x^{2}+13x+10}{x^{2}+5x+4}
Expand \left(x+1\right)\left(x+4\right).
\frac{\left(x+2\right)\left(x+4\right)}{\left(x+1\right)\left(x+4\right)}+\frac{\left(5x+2\right)\left(x+1\right)}{\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+1 and x+4 is \left(x+1\right)\left(x+4\right). Multiply \frac{x+2}{x+1} times \frac{x+4}{x+4}. Multiply \frac{5x+2}{x+4} times \frac{x+1}{x+1}.
\frac{\left(x+2\right)\left(x+4\right)+\left(5x+2\right)\left(x+1\right)}{\left(x+1\right)\left(x+4\right)}
Since \frac{\left(x+2\right)\left(x+4\right)}{\left(x+1\right)\left(x+4\right)} and \frac{\left(5x+2\right)\left(x+1\right)}{\left(x+1\right)\left(x+4\right)} have the same denominator, add them by adding their numerators.
\frac{x^{2}+4x+2x+8+5x^{2}+5x+2x+2}{\left(x+1\right)\left(x+4\right)}
Do the multiplications in \left(x+2\right)\left(x+4\right)+\left(5x+2\right)\left(x+1\right).
\frac{6x^{2}+13x+10}{\left(x+1\right)\left(x+4\right)}
Combine like terms in x^{2}+4x+2x+8+5x^{2}+5x+2x+2.
\frac{6x^{2}+13x+10}{x^{2}+5x+4}
Expand \left(x+1\right)\left(x+4\right).
Examples
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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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