Evaluate
\frac{6}{\left(3x+2\right)\left(3x+11\right)}
Expand
\frac{6}{\left(3x+2\right)\left(3x+11\right)}
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\frac{\left(x+3\right)\left(3x+2\right)}{\left(3x+2\right)\left(3x+11\right)}-\frac{x\left(3x+11\right)}{\left(3x+2\right)\left(3x+11\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x+11 and 2+3x is \left(3x+2\right)\left(3x+11\right). Multiply \frac{x+3}{3x+11} times \frac{3x+2}{3x+2}. Multiply \frac{x}{2+3x} times \frac{3x+11}{3x+11}.
\frac{\left(x+3\right)\left(3x+2\right)-x\left(3x+11\right)}{\left(3x+2\right)\left(3x+11\right)}
Since \frac{\left(x+3\right)\left(3x+2\right)}{\left(3x+2\right)\left(3x+11\right)} and \frac{x\left(3x+11\right)}{\left(3x+2\right)\left(3x+11\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{2}+2x+9x+6-3x^{2}-11x}{\left(3x+2\right)\left(3x+11\right)}
Do the multiplications in \left(x+3\right)\left(3x+2\right)-x\left(3x+11\right).
\frac{6}{\left(3x+2\right)\left(3x+11\right)}
Combine like terms in 3x^{2}+2x+9x+6-3x^{2}-11x.
\frac{6}{9x^{2}+39x+22}
Expand \left(3x+2\right)\left(3x+11\right).
\frac{\left(x+3\right)\left(3x+2\right)}{\left(3x+2\right)\left(3x+11\right)}-\frac{x\left(3x+11\right)}{\left(3x+2\right)\left(3x+11\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x+11 and 2+3x is \left(3x+2\right)\left(3x+11\right). Multiply \frac{x+3}{3x+11} times \frac{3x+2}{3x+2}. Multiply \frac{x}{2+3x} times \frac{3x+11}{3x+11}.
\frac{\left(x+3\right)\left(3x+2\right)-x\left(3x+11\right)}{\left(3x+2\right)\left(3x+11\right)}
Since \frac{\left(x+3\right)\left(3x+2\right)}{\left(3x+2\right)\left(3x+11\right)} and \frac{x\left(3x+11\right)}{\left(3x+2\right)\left(3x+11\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{2}+2x+9x+6-3x^{2}-11x}{\left(3x+2\right)\left(3x+11\right)}
Do the multiplications in \left(x+3\right)\left(3x+2\right)-x\left(3x+11\right).
\frac{6}{\left(3x+2\right)\left(3x+11\right)}
Combine like terms in 3x^{2}+2x+9x+6-3x^{2}-11x.
\frac{6}{9x^{2}+39x+22}
Expand \left(3x+2\right)\left(3x+11\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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