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\frac{3\times 2\left(x-2\right)}{2\left(x-2\right)\left(2x+7\right)}-\frac{5\left(2x+7\right)}{2\left(x-2\right)\left(2x+7\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x+7 and 2\left(x-2\right) is 2\left(x-2\right)\left(2x+7\right). Multiply \frac{3}{2x+7} times \frac{2\left(x-2\right)}{2\left(x-2\right)}. Multiply \frac{5}{2\left(x-2\right)} times \frac{2x+7}{2x+7}.
\frac{3\times 2\left(x-2\right)-5\left(2x+7\right)}{2\left(x-2\right)\left(2x+7\right)}
Since \frac{3\times 2\left(x-2\right)}{2\left(x-2\right)\left(2x+7\right)} and \frac{5\left(2x+7\right)}{2\left(x-2\right)\left(2x+7\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{6x-12-10x-35}{2\left(x-2\right)\left(2x+7\right)}
Do the multiplications in 3\times 2\left(x-2\right)-5\left(2x+7\right).
\frac{-4x-47}{2\left(x-2\right)\left(2x+7\right)}
Combine like terms in 6x-12-10x-35.
\frac{-4x-47}{4x^{2}+6x-28}
Expand 2\left(x-2\right)\left(2x+7\right).
\frac{3\times 2\left(x-2\right)}{2\left(x-2\right)\left(2x+7\right)}-\frac{5\left(2x+7\right)}{2\left(x-2\right)\left(2x+7\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x+7 and 2\left(x-2\right) is 2\left(x-2\right)\left(2x+7\right). Multiply \frac{3}{2x+7} times \frac{2\left(x-2\right)}{2\left(x-2\right)}. Multiply \frac{5}{2\left(x-2\right)} times \frac{2x+7}{2x+7}.
\frac{3\times 2\left(x-2\right)-5\left(2x+7\right)}{2\left(x-2\right)\left(2x+7\right)}
Since \frac{3\times 2\left(x-2\right)}{2\left(x-2\right)\left(2x+7\right)} and \frac{5\left(2x+7\right)}{2\left(x-2\right)\left(2x+7\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{6x-12-10x-35}{2\left(x-2\right)\left(2x+7\right)}
Do the multiplications in 3\times 2\left(x-2\right)-5\left(2x+7\right).
\frac{-4x-47}{2\left(x-2\right)\left(2x+7\right)}
Combine like terms in 6x-12-10x-35.
\frac{-4x-47}{4x^{2}+6x-28}
Expand 2\left(x-2\right)\left(2x+7\right).