What is the limit as x approaches 5 of (x^2-3x-10)/(x^2-4x-5) ?

The limit as x approaches 5 of (x^2-3x-10)/(x^2-4x-5) is 7/6

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limit as x approaches 5 of (x^2-3x-10)/(x^2-4x-5)

x \to 5 lim (\frac{x ^{2} - 3 x - 10}{x ^{2} - 4 x - 5})

\frac{7}{6}

Decimal Notation

1.16666 \dots

Solution steps

x \to 5 lim (\frac{x ^{2} - 3 x - 10}{x ^{2} - 4 x - 5})

Simplify

\frac{x ^{2} - 3 x - 10}{x ^{2} - 4 x - 5} : \frac{x + 2}{x + 1}

= x \to 5 lim (\frac{x + 2}{x + 1})

Plug in the value

x = 5

= \frac{5 + 2}{5 + 1}

Simplify

= \frac{7}{6}

x \to 2 lim ((x - 2)^{(x - 2)})

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

x \to 4 lim (0)

x \to \infty lim ((\frac{x + 3}{x})^{2 x - 7})

x \to 1 + lim (\frac{1}{x ^{2} + 2 x - 3})

What is the limit as x approaches 5 of (x^2-3x-10)/(x^2-4x-5) ?
The limit as x approaches 5 of (x^2-3x-10)/(x^2-4x-5) is 7/6