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\frac{5}{3x}-\frac{10}{3\left(2x+3\right)}
Factor 6x+9.
\frac{5\left(2x+3\right)}{3x\left(2x+3\right)}-\frac{10x}{3x\left(2x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x and 3\left(2x+3\right) is 3x\left(2x+3\right). Multiply \frac{5}{3x} times \frac{2x+3}{2x+3}. Multiply \frac{10}{3\left(2x+3\right)} times \frac{x}{x}.
\frac{5\left(2x+3\right)-10x}{3x\left(2x+3\right)}
Since \frac{5\left(2x+3\right)}{3x\left(2x+3\right)} and \frac{10x}{3x\left(2x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{10x+15-10x}{3x\left(2x+3\right)}
Do the multiplications in 5\left(2x+3\right)-10x.
\frac{15}{3x\left(2x+3\right)}
Combine like terms in 10x+15-10x.
\frac{15}{6x^{2}+9x}
Expand 3x\left(2x+3\right).