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To add or subtract expressions, expand them to make their denominators the same. Least common multiple of and is . Multiply times . Multiply times .
Since and have the same denominator, add them by adding their numerators.
Do the multiplications in .
Combine like terms in .
Expand .
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\frac{24\left(3x+1\right)}{\left(x-3\right)\left(3x+1\right)}+\frac{15\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and 3x+1 is \left(x-3\right)\left(3x+1\right). Multiply \frac{24}{x-3} times \frac{3x+1}{3x+1}. Multiply \frac{15}{3x+1} times \frac{x-3}{x-3}.
\frac{24\left(3x+1\right)+15\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)}
Since \frac{24\left(3x+1\right)}{\left(x-3\right)\left(3x+1\right)} and \frac{15\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)} have the same denominator, add them by adding their numerators.
\frac{72x+24+15x-45}{\left(x-3\right)\left(3x+1\right)}
Do the multiplications in 24\left(3x+1\right)+15\left(x-3\right).
\frac{87x-21}{\left(x-3\right)\left(3x+1\right)}
Combine like terms in 72x+24+15x-45.
\frac{87x-21}{3x^{2}-8x-3}
Expand \left(x-3\right)\left(3x+1\right).
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