Evaluate
\frac{30}{\left(x-3\right)\left(x+4\right)}
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\frac{30}{\left(x-3\right)\left(x+4\right)}
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\frac{\left(2x+11\right)\times 3}{\left(x-3\right)\left(x+4\right)}+\frac{2x+1}{4+x}\times \frac{3}{3-x}
Multiply \frac{2x+11}{x-3} times \frac{3}{x+4} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(2x+11\right)\times 3}{\left(x-3\right)\left(x+4\right)}+\frac{\left(2x+1\right)\times 3}{\left(4+x\right)\left(3-x\right)}
Multiply \frac{2x+1}{4+x} times \frac{3}{3-x} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(2x+11\right)\times 3}{\left(x-3\right)\left(x+4\right)}+\frac{-\left(2x+1\right)\times 3}{\left(x-3\right)\left(x+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)\left(x+4\right) and \left(4+x\right)\left(3-x\right) is \left(x-3\right)\left(x+4\right). Multiply \frac{\left(2x+1\right)\times 3}{\left(4+x\right)\left(3-x\right)} times \frac{-1}{-1}.
\frac{\left(2x+11\right)\times 3-\left(2x+1\right)\times 3}{\left(x-3\right)\left(x+4\right)}
Since \frac{\left(2x+11\right)\times 3}{\left(x-3\right)\left(x+4\right)} and \frac{-\left(2x+1\right)\times 3}{\left(x-3\right)\left(x+4\right)} have the same denominator, add them by adding their numerators.
\frac{6x+33-6x-3}{\left(x-3\right)\left(x+4\right)}
Do the multiplications in \left(2x+11\right)\times 3-\left(2x+1\right)\times 3.
\frac{30}{\left(x-3\right)\left(x+4\right)}
Combine like terms in 6x+33-6x-3.
\frac{30}{x^{2}+x-12}
Expand \left(x-3\right)\left(x+4\right).
\frac{\left(2x+11\right)\times 3}{\left(x-3\right)\left(x+4\right)}+\frac{2x+1}{4+x}\times \frac{3}{3-x}
Multiply \frac{2x+11}{x-3} times \frac{3}{x+4} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(2x+11\right)\times 3}{\left(x-3\right)\left(x+4\right)}+\frac{\left(2x+1\right)\times 3}{\left(4+x\right)\left(3-x\right)}
Multiply \frac{2x+1}{4+x} times \frac{3}{3-x} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(2x+11\right)\times 3}{\left(x-3\right)\left(x+4\right)}+\frac{-\left(2x+1\right)\times 3}{\left(x-3\right)\left(x+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)\left(x+4\right) and \left(4+x\right)\left(3-x\right) is \left(x-3\right)\left(x+4\right). Multiply \frac{\left(2x+1\right)\times 3}{\left(4+x\right)\left(3-x\right)} times \frac{-1}{-1}.
\frac{\left(2x+11\right)\times 3-\left(2x+1\right)\times 3}{\left(x-3\right)\left(x+4\right)}
Since \frac{\left(2x+11\right)\times 3}{\left(x-3\right)\left(x+4\right)} and \frac{-\left(2x+1\right)\times 3}{\left(x-3\right)\left(x+4\right)} have the same denominator, add them by adding their numerators.
\frac{6x+33-6x-3}{\left(x-3\right)\left(x+4\right)}
Do the multiplications in \left(2x+11\right)\times 3-\left(2x+1\right)\times 3.
\frac{30}{\left(x-3\right)\left(x+4\right)}
Combine like terms in 6x+33-6x-3.
\frac{30}{x^{2}+x-12}
Expand \left(x-3\right)\left(x+4\right).
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