Evaluate
\frac{4\left(5x+7\right)}{\left(x+3\right)\left(x^{2}-4\right)}
Expand
\frac{4\left(5x+7\right)}{\left(x+3\right)\left(x^{2}-4\right)}
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\frac{6\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{3\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{9x-5}{x^{2}+x-6}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and 2+x is \left(x-2\right)\left(x+2\right). Multiply \frac{6}{x-2} times \frac{x+2}{x+2}. Multiply \frac{3}{2+x} times \frac{x-2}{x-2}.
\frac{6\left(x+2\right)+3\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{9x-5}{x^{2}+x-6}
Since \frac{6\left(x+2\right)}{\left(x-2\right)\left(x+2\right)} and \frac{3\left(x-2\right)}{\left(x-2\right)\left(x+2\right)} have the same denominator, add them by adding their numerators.
\frac{6x+12+3x-6}{\left(x-2\right)\left(x+2\right)}-\frac{9x-5}{x^{2}+x-6}
Do the multiplications in 6\left(x+2\right)+3\left(x-2\right).
\frac{9x+6}{\left(x-2\right)\left(x+2\right)}-\frac{9x-5}{x^{2}+x-6}
Combine like terms in 6x+12+3x-6.
\frac{9x+6}{\left(x-2\right)\left(x+2\right)}-\frac{9x-5}{\left(x-2\right)\left(x+3\right)}
Factor x^{2}+x-6.
\frac{\left(9x+6\right)\left(x+3\right)}{\left(x-2\right)\left(x+2\right)\left(x+3\right)}-\frac{\left(9x-5\right)\left(x+2\right)}{\left(x-2\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-2\right)\left(x+2\right) and \left(x-2\right)\left(x+3\right) is \left(x-2\right)\left(x+2\right)\left(x+3\right). Multiply \frac{9x+6}{\left(x-2\right)\left(x+2\right)} times \frac{x+3}{x+3}. Multiply \frac{9x-5}{\left(x-2\right)\left(x+3\right)} times \frac{x+2}{x+2}.
\frac{\left(9x+6\right)\left(x+3\right)-\left(9x-5\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(x+3\right)}
Since \frac{\left(9x+6\right)\left(x+3\right)}{\left(x-2\right)\left(x+2\right)\left(x+3\right)} and \frac{\left(9x-5\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{9x^{2}+27x+6x+18-9x^{2}-18x+5x+10}{\left(x-2\right)\left(x+2\right)\left(x+3\right)}
Do the multiplications in \left(9x+6\right)\left(x+3\right)-\left(9x-5\right)\left(x+2\right).
\frac{20x+28}{\left(x-2\right)\left(x+2\right)\left(x+3\right)}
Combine like terms in 9x^{2}+27x+6x+18-9x^{2}-18x+5x+10.
\frac{20x+28}{x^{3}+3x^{2}-4x-12}
Expand \left(x-2\right)\left(x+2\right)\left(x+3\right).
\frac{6\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{3\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{9x-5}{x^{2}+x-6}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and 2+x is \left(x-2\right)\left(x+2\right). Multiply \frac{6}{x-2} times \frac{x+2}{x+2}. Multiply \frac{3}{2+x} times \frac{x-2}{x-2}.
\frac{6\left(x+2\right)+3\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{9x-5}{x^{2}+x-6}
Since \frac{6\left(x+2\right)}{\left(x-2\right)\left(x+2\right)} and \frac{3\left(x-2\right)}{\left(x-2\right)\left(x+2\right)} have the same denominator, add them by adding their numerators.
\frac{6x+12+3x-6}{\left(x-2\right)\left(x+2\right)}-\frac{9x-5}{x^{2}+x-6}
Do the multiplications in 6\left(x+2\right)+3\left(x-2\right).
\frac{9x+6}{\left(x-2\right)\left(x+2\right)}-\frac{9x-5}{x^{2}+x-6}
Combine like terms in 6x+12+3x-6.
\frac{9x+6}{\left(x-2\right)\left(x+2\right)}-\frac{9x-5}{\left(x-2\right)\left(x+3\right)}
Factor x^{2}+x-6.
\frac{\left(9x+6\right)\left(x+3\right)}{\left(x-2\right)\left(x+2\right)\left(x+3\right)}-\frac{\left(9x-5\right)\left(x+2\right)}{\left(x-2\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-2\right)\left(x+2\right) and \left(x-2\right)\left(x+3\right) is \left(x-2\right)\left(x+2\right)\left(x+3\right). Multiply \frac{9x+6}{\left(x-2\right)\left(x+2\right)} times \frac{x+3}{x+3}. Multiply \frac{9x-5}{\left(x-2\right)\left(x+3\right)} times \frac{x+2}{x+2}.
\frac{\left(9x+6\right)\left(x+3\right)-\left(9x-5\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(x+3\right)}
Since \frac{\left(9x+6\right)\left(x+3\right)}{\left(x-2\right)\left(x+2\right)\left(x+3\right)} and \frac{\left(9x-5\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{9x^{2}+27x+6x+18-9x^{2}-18x+5x+10}{\left(x-2\right)\left(x+2\right)\left(x+3\right)}
Do the multiplications in \left(9x+6\right)\left(x+3\right)-\left(9x-5\right)\left(x+2\right).
\frac{20x+28}{\left(x-2\right)\left(x+2\right)\left(x+3\right)}
Combine like terms in 9x^{2}+27x+6x+18-9x^{2}-18x+5x+10.
\frac{20x+28}{x^{3}+3x^{2}-4x-12}
Expand \left(x-2\right)\left(x+2\right)\left(x+3\right).
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
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}