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-\frac{2\left(13x+14\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}
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-\frac{2\left(13x+14\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}
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\frac{4x+5}{\left(5x-1\right)\left(3x+2\right)}-\frac{2x+3}{\left(4x-5\right)\left(3x+2\right)}-\frac{2x+3}{20x^{2}-29x+5}
Factor 15x^{2}+7x-2. Factor 12x^{2}-7x-10.
\frac{\left(4x+5\right)\left(4x-5\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}-\frac{\left(2x+3\right)\left(5x-1\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}-\frac{2x+3}{20x^{2}-29x+5}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(5x-1\right)\left(3x+2\right) and \left(4x-5\right)\left(3x+2\right) is \left(4x-5\right)\left(5x-1\right)\left(3x+2\right). Multiply \frac{4x+5}{\left(5x-1\right)\left(3x+2\right)} times \frac{4x-5}{4x-5}. Multiply \frac{2x+3}{\left(4x-5\right)\left(3x+2\right)} times \frac{5x-1}{5x-1}.
\frac{\left(4x+5\right)\left(4x-5\right)-\left(2x+3\right)\left(5x-1\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}-\frac{2x+3}{20x^{2}-29x+5}
Since \frac{\left(4x+5\right)\left(4x-5\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)} and \frac{\left(2x+3\right)\left(5x-1\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{16x^{2}-20x+20x-25-10x^{2}+2x-15x+3}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}-\frac{2x+3}{20x^{2}-29x+5}
Do the multiplications in \left(4x+5\right)\left(4x-5\right)-\left(2x+3\right)\left(5x-1\right).
\frac{6x^{2}-13x-22}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}-\frac{2x+3}{20x^{2}-29x+5}
Combine like terms in 16x^{2}-20x+20x-25-10x^{2}+2x-15x+3.
\frac{6x^{2}-13x-22}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}-\frac{2x+3}{\left(4x-5\right)\left(5x-1\right)}
Factor 20x^{2}-29x+5.
\frac{6x^{2}-13x-22}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}-\frac{\left(2x+3\right)\left(3x+2\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(4x-5\right)\left(5x-1\right)\left(3x+2\right) and \left(4x-5\right)\left(5x-1\right) is \left(4x-5\right)\left(5x-1\right)\left(3x+2\right). Multiply \frac{2x+3}{\left(4x-5\right)\left(5x-1\right)} times \frac{3x+2}{3x+2}.
\frac{6x^{2}-13x-22-\left(2x+3\right)\left(3x+2\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}
Since \frac{6x^{2}-13x-22}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)} and \frac{\left(2x+3\right)\left(3x+2\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{6x^{2}-13x-22-6x^{2}-4x-9x-6}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}
Do the multiplications in 6x^{2}-13x-22-\left(2x+3\right)\left(3x+2\right).
\frac{-26x-28}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}
Combine like terms in 6x^{2}-13x-22-6x^{2}-4x-9x-6.
\frac{-26x-28}{60x^{3}-47x^{2}-43x+10}
Expand \left(4x-5\right)\left(5x-1\right)\left(3x+2\right).
\frac{4x+5}{\left(5x-1\right)\left(3x+2\right)}-\frac{2x+3}{\left(4x-5\right)\left(3x+2\right)}-\frac{2x+3}{20x^{2}-29x+5}
Factor 15x^{2}+7x-2. Factor 12x^{2}-7x-10.
\frac{\left(4x+5\right)\left(4x-5\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}-\frac{\left(2x+3\right)\left(5x-1\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}-\frac{2x+3}{20x^{2}-29x+5}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(5x-1\right)\left(3x+2\right) and \left(4x-5\right)\left(3x+2\right) is \left(4x-5\right)\left(5x-1\right)\left(3x+2\right). Multiply \frac{4x+5}{\left(5x-1\right)\left(3x+2\right)} times \frac{4x-5}{4x-5}. Multiply \frac{2x+3}{\left(4x-5\right)\left(3x+2\right)} times \frac{5x-1}{5x-1}.
\frac{\left(4x+5\right)\left(4x-5\right)-\left(2x+3\right)\left(5x-1\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}-\frac{2x+3}{20x^{2}-29x+5}
Since \frac{\left(4x+5\right)\left(4x-5\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)} and \frac{\left(2x+3\right)\left(5x-1\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{16x^{2}-20x+20x-25-10x^{2}+2x-15x+3}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}-\frac{2x+3}{20x^{2}-29x+5}
Do the multiplications in \left(4x+5\right)\left(4x-5\right)-\left(2x+3\right)\left(5x-1\right).
\frac{6x^{2}-13x-22}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}-\frac{2x+3}{20x^{2}-29x+5}
Combine like terms in 16x^{2}-20x+20x-25-10x^{2}+2x-15x+3.
\frac{6x^{2}-13x-22}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}-\frac{2x+3}{\left(4x-5\right)\left(5x-1\right)}
Factor 20x^{2}-29x+5.
\frac{6x^{2}-13x-22}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}-\frac{\left(2x+3\right)\left(3x+2\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(4x-5\right)\left(5x-1\right)\left(3x+2\right) and \left(4x-5\right)\left(5x-1\right) is \left(4x-5\right)\left(5x-1\right)\left(3x+2\right). Multiply \frac{2x+3}{\left(4x-5\right)\left(5x-1\right)} times \frac{3x+2}{3x+2}.
\frac{6x^{2}-13x-22-\left(2x+3\right)\left(3x+2\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}
Since \frac{6x^{2}-13x-22}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)} and \frac{\left(2x+3\right)\left(3x+2\right)}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{6x^{2}-13x-22-6x^{2}-4x-9x-6}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}
Do the multiplications in 6x^{2}-13x-22-\left(2x+3\right)\left(3x+2\right).
\frac{-26x-28}{\left(4x-5\right)\left(5x-1\right)\left(3x+2\right)}
Combine like terms in 6x^{2}-13x-22-6x^{2}-4x-9x-6.
\frac{-26x-28}{60x^{3}-47x^{2}-43x+10}
Expand \left(4x-5\right)\left(5x-1\right)\left(3x+2\right).
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