Evaluate
\frac{3x-4}{\left(x-3\right)\left(x+2\right)}
Expand
\frac{3x-4}{\left(x-3\right)\left(x+2\right)}
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\frac{x+2}{\left(x-3\right)\left(x+2\right)}+\frac{2}{x+2}
Factor the expressions that are not already factored in \frac{x+2}{x^{2}-x-6}.
\frac{1}{x-3}+\frac{2}{x+2}
Cancel out x+2 in both numerator and denominator.
\frac{x+2}{\left(x-3\right)\left(x+2\right)}+\frac{2\left(x-3\right)}{\left(x-3\right)\left(x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and x+2 is \left(x-3\right)\left(x+2\right). Multiply \frac{1}{x-3} times \frac{x+2}{x+2}. Multiply \frac{2}{x+2} times \frac{x-3}{x-3}.
\frac{x+2+2\left(x-3\right)}{\left(x-3\right)\left(x+2\right)}
Since \frac{x+2}{\left(x-3\right)\left(x+2\right)} and \frac{2\left(x-3\right)}{\left(x-3\right)\left(x+2\right)} have the same denominator, add them by adding their numerators.
\frac{x+2+2x-6}{\left(x-3\right)\left(x+2\right)}
Do the multiplications in x+2+2\left(x-3\right).
\frac{3x-4}{\left(x-3\right)\left(x+2\right)}
Combine like terms in x+2+2x-6.
\frac{3x-4}{x^{2}-x-6}
Expand \left(x-3\right)\left(x+2\right).
\frac{x+2}{\left(x-3\right)\left(x+2\right)}+\frac{2}{x+2}
Factor the expressions that are not already factored in \frac{x+2}{x^{2}-x-6}.
\frac{1}{x-3}+\frac{2}{x+2}
Cancel out x+2 in both numerator and denominator.
\frac{x+2}{\left(x-3\right)\left(x+2\right)}+\frac{2\left(x-3\right)}{\left(x-3\right)\left(x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and x+2 is \left(x-3\right)\left(x+2\right). Multiply \frac{1}{x-3} times \frac{x+2}{x+2}. Multiply \frac{2}{x+2} times \frac{x-3}{x-3}.
\frac{x+2+2\left(x-3\right)}{\left(x-3\right)\left(x+2\right)}
Since \frac{x+2}{\left(x-3\right)\left(x+2\right)} and \frac{2\left(x-3\right)}{\left(x-3\right)\left(x+2\right)} have the same denominator, add them by adding their numerators.
\frac{x+2+2x-6}{\left(x-3\right)\left(x+2\right)}
Do the multiplications in x+2+2\left(x-3\right).
\frac{3x-4}{\left(x-3\right)\left(x+2\right)}
Combine like terms in x+2+2x-6.
\frac{3x-4}{x^{2}-x-6}
Expand \left(x-3\right)\left(x+2\right).
Examples
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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}