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\frac{6x\left(2x+5\right)}{\left(3x-1\right)\left(2x+5\right)}-\frac{4x\left(3x-1\right)}{\left(3x-1\right)\left(2x+5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x-1 and 2x+5 is \left(3x-1\right)\left(2x+5\right). Multiply \frac{6x}{3x-1} times \frac{2x+5}{2x+5}. Multiply \frac{4x}{2x+5} times \frac{3x-1}{3x-1}.
\frac{6x\left(2x+5\right)-4x\left(3x-1\right)}{\left(3x-1\right)\left(2x+5\right)}
Since \frac{6x\left(2x+5\right)}{\left(3x-1\right)\left(2x+5\right)} and \frac{4x\left(3x-1\right)}{\left(3x-1\right)\left(2x+5\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{12x^{2}+30x-12x^{2}+4x}{\left(3x-1\right)\left(2x+5\right)}
Do the multiplications in 6x\left(2x+5\right)-4x\left(3x-1\right).
\frac{34x}{\left(3x-1\right)\left(2x+5\right)}
Combine like terms in 12x^{2}+30x-12x^{2}+4x.
\frac{34x}{6x^{2}+13x-5}
Expand \left(3x-1\right)\left(2x+5\right).