Evaluate
-\frac{23x+30}{x^{2}-36}
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-\frac{23x+30}{x^{2}-36}
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\frac{\left(x-3\right)\left(x-6\right)}{\left(x-6\right)\left(x+6\right)}-\frac{\left(x+8\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+6 and x-6 is \left(x-6\right)\left(x+6\right). Multiply \frac{x-3}{x+6} times \frac{x-6}{x-6}. Multiply \frac{x+8}{x-6} times \frac{x+6}{x+6}.
\frac{\left(x-3\right)\left(x-6\right)-\left(x+8\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}
Since \frac{\left(x-3\right)\left(x-6\right)}{\left(x-6\right)\left(x+6\right)} and \frac{\left(x+8\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-6x-3x+18-x^{2}-6x-8x-48}{\left(x-6\right)\left(x+6\right)}
Do the multiplications in \left(x-3\right)\left(x-6\right)-\left(x+8\right)\left(x+6\right).
\frac{-23x-30}{\left(x-6\right)\left(x+6\right)}
Combine like terms in x^{2}-6x-3x+18-x^{2}-6x-8x-48.
\frac{-23x-30}{x^{2}-36}
Expand \left(x-6\right)\left(x+6\right).
\frac{\left(x-3\right)\left(x-6\right)}{\left(x-6\right)\left(x+6\right)}-\frac{\left(x+8\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+6 and x-6 is \left(x-6\right)\left(x+6\right). Multiply \frac{x-3}{x+6} times \frac{x-6}{x-6}. Multiply \frac{x+8}{x-6} times \frac{x+6}{x+6}.
\frac{\left(x-3\right)\left(x-6\right)-\left(x+8\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}
Since \frac{\left(x-3\right)\left(x-6\right)}{\left(x-6\right)\left(x+6\right)} and \frac{\left(x+8\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-6x-3x+18-x^{2}-6x-8x-48}{\left(x-6\right)\left(x+6\right)}
Do the multiplications in \left(x-3\right)\left(x-6\right)-\left(x+8\right)\left(x+6\right).
\frac{-23x-30}{\left(x-6\right)\left(x+6\right)}
Combine like terms in x^{2}-6x-3x+18-x^{2}-6x-8x-48.
\frac{-23x-30}{x^{2}-36}
Expand \left(x-6\right)\left(x+6\right).
Examples
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y = 3x + 4
Arithmetic
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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
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