What is the limit as x approaches 8 of (x^2-8x)/(x^2-7x-8) ?

The limit as x approaches 8 of (x^2-8x)/(x^2-7x-8) is 8/9

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limit as x approaches 8 of (x^2-8x)/(x^2-7x-8)

x \to 8 lim (\frac{x ^{2} - 8 x}{x ^{2} - 7 x - 8})

\frac{8}{9}

Decimal Notation

0.88888 \dots

Solution steps

x \to 8 lim (\frac{x ^{2} - 8 x}{x ^{2} - 7 x - 8})

Simplify

\frac{x ^{2} - 8 x}{x ^{2} - 7 x - 8} : \frac{x}{x + 1}

= x \to 8 lim (\frac{x}{x + 1})

Plug in the value

x = 8

= \frac{8}{8 + 1}

Simplify

= \frac{8}{9}

x \to - 5 lim (x^{2} - 2 x + 3)

x \to 5 lim (3 x - 5)

x \to 40 lim (15)

x \to 5 - lim (- \frac{3}{x + 5})

x \to 1 lim (\frac{ln ( 1 + x )}{x})

What is the limit as x approaches 8 of (x^2-8x)/(x^2-7x-8) ?
The limit as x approaches 8 of (x^2-8x)/(x^2-7x-8) is 8/9