Evaluate
\frac{8x-131}{17\left(2x-3\right)\left(x+2\right)}
Expand
\frac{8x-131}{17\left(2x-3\right)\left(x+2\right)}
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\frac{-2\times 17\left(x+2\right)}{17\left(2x-3\right)\left(x+2\right)}+\frac{21\left(2x-3\right)}{17\left(2x-3\right)\left(x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x-3 and 17\left(x+2\right) is 17\left(2x-3\right)\left(x+2\right). Multiply \frac{-2}{2x-3} times \frac{17\left(x+2\right)}{17\left(x+2\right)}. Multiply \frac{21}{17\left(x+2\right)} times \frac{2x-3}{2x-3}.
\frac{-2\times 17\left(x+2\right)+21\left(2x-3\right)}{17\left(2x-3\right)\left(x+2\right)}
Since \frac{-2\times 17\left(x+2\right)}{17\left(2x-3\right)\left(x+2\right)} and \frac{21\left(2x-3\right)}{17\left(2x-3\right)\left(x+2\right)} have the same denominator, add them by adding their numerators.
\frac{-34x-68+42x-63}{17\left(2x-3\right)\left(x+2\right)}
Do the multiplications in -2\times 17\left(x+2\right)+21\left(2x-3\right).
\frac{8x-131}{17\left(2x-3\right)\left(x+2\right)}
Combine like terms in -34x-68+42x-63.
\frac{8x-131}{34x^{2}+17x-102}
Expand 17\left(2x-3\right)\left(x+2\right).
\frac{-2\times 17\left(x+2\right)}{17\left(2x-3\right)\left(x+2\right)}+\frac{21\left(2x-3\right)}{17\left(2x-3\right)\left(x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x-3 and 17\left(x+2\right) is 17\left(2x-3\right)\left(x+2\right). Multiply \frac{-2}{2x-3} times \frac{17\left(x+2\right)}{17\left(x+2\right)}. Multiply \frac{21}{17\left(x+2\right)} times \frac{2x-3}{2x-3}.
\frac{-2\times 17\left(x+2\right)+21\left(2x-3\right)}{17\left(2x-3\right)\left(x+2\right)}
Since \frac{-2\times 17\left(x+2\right)}{17\left(2x-3\right)\left(x+2\right)} and \frac{21\left(2x-3\right)}{17\left(2x-3\right)\left(x+2\right)} have the same denominator, add them by adding their numerators.
\frac{-34x-68+42x-63}{17\left(2x-3\right)\left(x+2\right)}
Do the multiplications in -2\times 17\left(x+2\right)+21\left(2x-3\right).
\frac{8x-131}{17\left(2x-3\right)\left(x+2\right)}
Combine like terms in -34x-68+42x-63.
\frac{8x-131}{34x^{2}+17x-102}
Expand 17\left(2x-3\right)\left(x+2\right).
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