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\frac{x+1}{\left(x-3\right)\left(x+4\right)}-\frac{x-3}{\left(x+3\right)\left(x+4\right)}
Factor x^{2}+x-12. Factor x^{2}+7x+12.
\frac{\left(x+1\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}-\frac{\left(x-3\right)\left(x-3\right)}{\left(x-3\right)\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(x+3\right)\left(x+4\right) is \left(x-3\right)\left(x+3\right)\left(x+4\right). Multiply \frac{x+1}{\left(x-3\right)\left(x+4\right)} times \frac{x+3}{x+3}. Multiply \frac{x-3}{\left(x+3\right)\left(x+4\right)} times \frac{x-3}{x-3}.
\frac{\left(x+1\right)\left(x+3\right)-\left(x-3\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}
Since \frac{\left(x+1\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)} and \frac{\left(x-3\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+3x+x+3-x^{2}+3x+3x-9}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}
Do the multiplications in \left(x+1\right)\left(x+3\right)-\left(x-3\right)\left(x-3\right).
\frac{10x-6}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}
Combine like terms in x^{2}+3x+x+3-x^{2}+3x+3x-9.
\frac{10x-6}{x^{3}+4x^{2}-9x-36}
Expand \left(x-3\right)\left(x+3\right)\left(x+4\right).
\frac{x+1}{\left(x-3\right)\left(x+4\right)}-\frac{x-3}{\left(x+3\right)\left(x+4\right)}
Factor x^{2}+x-12. Factor x^{2}+7x+12.
\frac{\left(x+1\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}-\frac{\left(x-3\right)\left(x-3\right)}{\left(x-3\right)\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(x+3\right)\left(x+4\right) is \left(x-3\right)\left(x+3\right)\left(x+4\right). Multiply \frac{x+1}{\left(x-3\right)\left(x+4\right)} times \frac{x+3}{x+3}. Multiply \frac{x-3}{\left(x+3\right)\left(x+4\right)} times \frac{x-3}{x-3}.
\frac{\left(x+1\right)\left(x+3\right)-\left(x-3\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}
Since \frac{\left(x+1\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)} and \frac{\left(x-3\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+3x+x+3-x^{2}+3x+3x-9}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}
Do the multiplications in \left(x+1\right)\left(x+3\right)-\left(x-3\right)\left(x-3\right).
\frac{10x-6}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}
Combine like terms in x^{2}+3x+x+3-x^{2}+3x+3x-9.
\frac{10x-6}{x^{3}+4x^{2}-9x-36}
Expand \left(x-3\right)\left(x+3\right)\left(x+4\right).