Evaluate
\frac{5x^{2}+24x-26}{\left(5x-4\right)\left(5x+2\right)}
Expand
\frac{5x^{2}+24x-26}{\left(5x-4\right)\left(5x+2\right)}
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\frac{\left(3x+7\right)\left(5x-4\right)}{\left(5x-4\right)\left(5x+2\right)}-\frac{\left(2x-1\right)\left(5x+2\right)}{\left(5x-4\right)\left(5x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5x+2 and 5x-4 is \left(5x-4\right)\left(5x+2\right). Multiply \frac{3x+7}{5x+2} times \frac{5x-4}{5x-4}. Multiply \frac{2x-1}{5x-4} times \frac{5x+2}{5x+2}.
\frac{\left(3x+7\right)\left(5x-4\right)-\left(2x-1\right)\left(5x+2\right)}{\left(5x-4\right)\left(5x+2\right)}
Since \frac{\left(3x+7\right)\left(5x-4\right)}{\left(5x-4\right)\left(5x+2\right)} and \frac{\left(2x-1\right)\left(5x+2\right)}{\left(5x-4\right)\left(5x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{15x^{2}-12x+35x-28-10x^{2}-4x+5x+2}{\left(5x-4\right)\left(5x+2\right)}
Do the multiplications in \left(3x+7\right)\left(5x-4\right)-\left(2x-1\right)\left(5x+2\right).
\frac{5x^{2}+24x-26}{\left(5x-4\right)\left(5x+2\right)}
Combine like terms in 15x^{2}-12x+35x-28-10x^{2}-4x+5x+2.
\frac{5x^{2}+24x-26}{25x^{2}-10x-8}
Expand \left(5x-4\right)\left(5x+2\right).
\frac{\left(3x+7\right)\left(5x-4\right)}{\left(5x-4\right)\left(5x+2\right)}-\frac{\left(2x-1\right)\left(5x+2\right)}{\left(5x-4\right)\left(5x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5x+2 and 5x-4 is \left(5x-4\right)\left(5x+2\right). Multiply \frac{3x+7}{5x+2} times \frac{5x-4}{5x-4}. Multiply \frac{2x-1}{5x-4} times \frac{5x+2}{5x+2}.
\frac{\left(3x+7\right)\left(5x-4\right)-\left(2x-1\right)\left(5x+2\right)}{\left(5x-4\right)\left(5x+2\right)}
Since \frac{\left(3x+7\right)\left(5x-4\right)}{\left(5x-4\right)\left(5x+2\right)} and \frac{\left(2x-1\right)\left(5x+2\right)}{\left(5x-4\right)\left(5x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{15x^{2}-12x+35x-28-10x^{2}-4x+5x+2}{\left(5x-4\right)\left(5x+2\right)}
Do the multiplications in \left(3x+7\right)\left(5x-4\right)-\left(2x-1\right)\left(5x+2\right).
\frac{5x^{2}+24x-26}{\left(5x-4\right)\left(5x+2\right)}
Combine like terms in 15x^{2}-12x+35x-28-10x^{2}-4x+5x+2.
\frac{5x^{2}+24x-26}{25x^{2}-10x-8}
Expand \left(5x-4\right)\left(5x+2\right).
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