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