Evaluate
\frac{5x-12}{\left(x-6\right)\left(x-3\right)}
Expand
\frac{5x-12}{\left(x-6\right)\left(x-3\right)}
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\frac{x\left(x-3\right)}{\left(x-6\right)\left(x-3\right)}-\frac{\left(x-2\right)\left(x-6\right)}{\left(x-6\right)\left(x-3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-6 and x-3 is \left(x-6\right)\left(x-3\right). Multiply \frac{x}{x-6} times \frac{x-3}{x-3}. Multiply \frac{x-2}{x-3} times \frac{x-6}{x-6}.
\frac{x\left(x-3\right)-\left(x-2\right)\left(x-6\right)}{\left(x-6\right)\left(x-3\right)}
Since \frac{x\left(x-3\right)}{\left(x-6\right)\left(x-3\right)} and \frac{\left(x-2\right)\left(x-6\right)}{\left(x-6\right)\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-3x-x^{2}+6x+2x-12}{\left(x-6\right)\left(x-3\right)}
Do the multiplications in x\left(x-3\right)-\left(x-2\right)\left(x-6\right).
\frac{5x-12}{\left(x-6\right)\left(x-3\right)}
Combine like terms in x^{2}-3x-x^{2}+6x+2x-12.
\frac{5x-12}{x^{2}-9x+18}
Expand \left(x-6\right)\left(x-3\right).
\frac{x\left(x-3\right)}{\left(x-6\right)\left(x-3\right)}-\frac{\left(x-2\right)\left(x-6\right)}{\left(x-6\right)\left(x-3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-6 and x-3 is \left(x-6\right)\left(x-3\right). Multiply \frac{x}{x-6} times \frac{x-3}{x-3}. Multiply \frac{x-2}{x-3} times \frac{x-6}{x-6}.
\frac{x\left(x-3\right)-\left(x-2\right)\left(x-6\right)}{\left(x-6\right)\left(x-3\right)}
Since \frac{x\left(x-3\right)}{\left(x-6\right)\left(x-3\right)} and \frac{\left(x-2\right)\left(x-6\right)}{\left(x-6\right)\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-3x-x^{2}+6x+2x-12}{\left(x-6\right)\left(x-3\right)}
Do the multiplications in x\left(x-3\right)-\left(x-2\right)\left(x-6\right).
\frac{5x-12}{\left(x-6\right)\left(x-3\right)}
Combine like terms in x^{2}-3x-x^{2}+6x+2x-12.
\frac{5x-12}{x^{2}-9x+18}
Expand \left(x-6\right)\left(x-3\right).
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Simultaneous equation
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Differentiation
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Integration
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Limits
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