Evaluate
\frac{-x^{2}+2x-29}{\left(x-8\right)\left(x-1\right)}
Expand
\frac{-x^{2}+2x-29}{\left(x-8\right)\left(x-1\right)}
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\frac{\left(-x-3\right)\left(x-1\right)}{\left(x-8\right)\left(x-1\right)}+\frac{4\left(x-8\right)}{\left(x-8\right)\left(x-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-8 and x-1 is \left(x-8\right)\left(x-1\right). Multiply \frac{-x-3}{x-8} times \frac{x-1}{x-1}. Multiply \frac{4}{x-1} times \frac{x-8}{x-8}.
\frac{\left(-x-3\right)\left(x-1\right)+4\left(x-8\right)}{\left(x-8\right)\left(x-1\right)}
Since \frac{\left(-x-3\right)\left(x-1\right)}{\left(x-8\right)\left(x-1\right)} and \frac{4\left(x-8\right)}{\left(x-8\right)\left(x-1\right)} have the same denominator, add them by adding their numerators.
\frac{-x^{2}+x-3x+3+4x-32}{\left(x-8\right)\left(x-1\right)}
Do the multiplications in \left(-x-3\right)\left(x-1\right)+4\left(x-8\right).
\frac{-x^{2}+2x-29}{\left(x-8\right)\left(x-1\right)}
Combine like terms in -x^{2}+x-3x+3+4x-32.
\frac{-x^{2}+2x-29}{x^{2}-9x+8}
Expand \left(x-8\right)\left(x-1\right).
\frac{\left(-x-3\right)\left(x-1\right)}{\left(x-8\right)\left(x-1\right)}+\frac{4\left(x-8\right)}{\left(x-8\right)\left(x-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-8 and x-1 is \left(x-8\right)\left(x-1\right). Multiply \frac{-x-3}{x-8} times \frac{x-1}{x-1}. Multiply \frac{4}{x-1} times \frac{x-8}{x-8}.
\frac{\left(-x-3\right)\left(x-1\right)+4\left(x-8\right)}{\left(x-8\right)\left(x-1\right)}
Since \frac{\left(-x-3\right)\left(x-1\right)}{\left(x-8\right)\left(x-1\right)} and \frac{4\left(x-8\right)}{\left(x-8\right)\left(x-1\right)} have the same denominator, add them by adding their numerators.
\frac{-x^{2}+x-3x+3+4x-32}{\left(x-8\right)\left(x-1\right)}
Do the multiplications in \left(-x-3\right)\left(x-1\right)+4\left(x-8\right).
\frac{-x^{2}+2x-29}{\left(x-8\right)\left(x-1\right)}
Combine like terms in -x^{2}+x-3x+3+4x-32.
\frac{-x^{2}+2x-29}{x^{2}-9x+8}
Expand \left(x-8\right)\left(x-1\right).
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Limits
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