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

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

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limit as x approaches-2 of ((x^2-3x-10))/((x^2+5x+6))

x \to - 2 lim (\frac{( x ^{2} - 3 x - 10 )}{( x ^{2} + 5 x + 6 )})

- 7

Solution steps

x \to - 2 lim (\frac{x ^{2} - 3 x - 10}{x ^{2} + 5 x + 6})

Simplify

\frac{x ^{2} - 3 x - 10}{x ^{2} + 5 x + 6} : \frac{x - 5}{x + 3}

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

Plug in the value

x = - 2

= \frac{- 2 - 5}{- 2 + 3}

Simplify

= - 7

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