Evaluate
-\frac{x^{2}+6x+4}{x^{2}-4}
Expand
-\frac{x^{2}+6x+4}{x^{2}-4}
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\frac{x+6}{\left(x-2\right)\left(x+2\right)}-\frac{x+5}{x-2}
Factor x^{2}-4.
\frac{x+6}{\left(x-2\right)\left(x+2\right)}-\frac{\left(x+5\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\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 x-2 is \left(x-2\right)\left(x+2\right). Multiply \frac{x+5}{x-2} times \frac{x+2}{x+2}.
\frac{x+6-\left(x+5\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}
Since \frac{x+6}{\left(x-2\right)\left(x+2\right)} and \frac{\left(x+5\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x+6-x^{2}-2x-5x-10}{\left(x-2\right)\left(x+2\right)}
Do the multiplications in x+6-\left(x+5\right)\left(x+2\right).
\frac{-6x-4-x^{2}}{\left(x-2\right)\left(x+2\right)}
Combine like terms in x+6-x^{2}-2x-5x-10.
\frac{-6x-4-x^{2}}{x^{2}-4}
Expand \left(x-2\right)\left(x+2\right).
\frac{x+6}{\left(x-2\right)\left(x+2\right)}-\frac{x+5}{x-2}
Factor x^{2}-4.
\frac{x+6}{\left(x-2\right)\left(x+2\right)}-\frac{\left(x+5\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\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 x-2 is \left(x-2\right)\left(x+2\right). Multiply \frac{x+5}{x-2} times \frac{x+2}{x+2}.
\frac{x+6-\left(x+5\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}
Since \frac{x+6}{\left(x-2\right)\left(x+2\right)} and \frac{\left(x+5\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x+6-x^{2}-2x-5x-10}{\left(x-2\right)\left(x+2\right)}
Do the multiplications in x+6-\left(x+5\right)\left(x+2\right).
\frac{-6x-4-x^{2}}{\left(x-2\right)\left(x+2\right)}
Combine like terms in x+6-x^{2}-2x-5x-10.
\frac{-6x-4-x^{2}}{x^{2}-4}
Expand \left(x-2\right)\left(x+2\right).
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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
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Limits
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