Evaluate
\frac{3x+11}{x^{2}-9}
Expand
\frac{3x+11}{x^{2}-9}
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\frac{2}{x-3}+\frac{x+5}{\left(x-3\right)\left(x+3\right)}
Factor x^{2}-9.
\frac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\frac{x+5}{\left(x-3\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and \left(x-3\right)\left(x+3\right) is \left(x-3\right)\left(x+3\right). Multiply \frac{2}{x-3} times \frac{x+3}{x+3}.
\frac{2\left(x+3\right)+x+5}{\left(x-3\right)\left(x+3\right)}
Since \frac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)} and \frac{x+5}{\left(x-3\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{2x+6+x+5}{\left(x-3\right)\left(x+3\right)}
Do the multiplications in 2\left(x+3\right)+x+5.
\frac{3x+11}{\left(x-3\right)\left(x+3\right)}
Combine like terms in 2x+6+x+5.
\frac{3x+11}{x^{2}-9}
Expand \left(x-3\right)\left(x+3\right).
\frac{2}{x-3}+\frac{x+5}{\left(x-3\right)\left(x+3\right)}
Factor x^{2}-9.
\frac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\frac{x+5}{\left(x-3\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and \left(x-3\right)\left(x+3\right) is \left(x-3\right)\left(x+3\right). Multiply \frac{2}{x-3} times \frac{x+3}{x+3}.
\frac{2\left(x+3\right)+x+5}{\left(x-3\right)\left(x+3\right)}
Since \frac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)} and \frac{x+5}{\left(x-3\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{2x+6+x+5}{\left(x-3\right)\left(x+3\right)}
Do the multiplications in 2\left(x+3\right)+x+5.
\frac{3x+11}{\left(x-3\right)\left(x+3\right)}
Combine like terms in 2x+6+x+5.
\frac{3x+11}{x^{2}-9}
Expand \left(x-3\right)\left(x+3\right).
Examples
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y = 3x + 4
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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}