Evaluate
\frac{1}{2x-19}
Expand
\frac{1}{2x-19}
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\frac{3x+10-\left(2x+6\right)}{2x^{2}-11x-76}
Since \frac{3x+10}{2x^{2}-11x-76} and \frac{2x+6}{2x^{2}-11x-76} have the same denominator, subtract them by subtracting their numerators.
\frac{3x+10-2x-6}{2x^{2}-11x-76}
Do the multiplications in 3x+10-\left(2x+6\right).
\frac{x+4}{2x^{2}-11x-76}
Combine like terms in 3x+10-2x-6.
\frac{x+4}{\left(2x-19\right)\left(x+4\right)}
Factor the expressions that are not already factored in \frac{x+4}{2x^{2}-11x-76}.
\frac{1}{2x-19}
Cancel out x+4 in both numerator and denominator.
\frac{3x+10-\left(2x+6\right)}{2x^{2}-11x-76}
Since \frac{3x+10}{2x^{2}-11x-76} and \frac{2x+6}{2x^{2}-11x-76} have the same denominator, subtract them by subtracting their numerators.
\frac{3x+10-2x-6}{2x^{2}-11x-76}
Do the multiplications in 3x+10-\left(2x+6\right).
\frac{x+4}{2x^{2}-11x-76}
Combine like terms in 3x+10-2x-6.
\frac{x+4}{\left(2x-19\right)\left(x+4\right)}
Factor the expressions that are not already factored in \frac{x+4}{2x^{2}-11x-76}.
\frac{1}{2x-19}
Cancel out x+4 in both numerator and denominator.
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Limits
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