# Step-by-step Solution

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$\frac{7}{15}$$\,\,\left(\approx 0.4666666666666667\right) ## Step-by-step explanation Problem to solve: \lim_{x\to5}\left(\frac{x^2+8x-9}{x^3-x^2+5x-5}\right) Choose the solving method 1 Evaluate the limit \lim_{x\to5}\left(\frac{x^2+8x-9}{x^3-x^2+5x-5}\right) by replacing all occurrences of x by 5 \frac{5^2+8\cdot 5-9}{5^3-1\cdot 5^2+5\cdot 5-5} 2 Simplifying, we get \frac{7}{15} ## Final Answer \frac{7}{15}$$\,\,\left(\approx 0.4666666666666667\right)$
$\lim_{x\to5}\left(\frac{x^2+8x-9}{x^3-x^2+5x-5}\right)$