What is the limit as x approaches 3 of ((x^2-2x-3))/(x^2-9) ?

The limit as x approaches 3 of ((x^2-2x-3))/(x^2-9) is 2/3

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limit as x approaches 3 of ((x^2-2x-3))/(x^2-9)

x \to 3 lim (\frac{( x ^{2} - 2 x - 3 )}{x ^{2} - 9})

\frac{2}{3}

Decimal Notation

0.66666 \dots

Solution steps

x \to 3 lim (\frac{x ^{2} - 2 x - 3}{x ^{2} - 9})

Simplify

\frac{x ^{2} - 2 x - 3}{x ^{2} - 9} : \frac{x + 1}{x + 3}

= x \to 3 lim (\frac{x + 1}{x + 3})

Plug in the value

x = 3

= \frac{3 + 1}{3 + 3}

Simplify

\frac{3 + 1}{3 + 3} : \frac{2}{3}

= \frac{2}{3}

y^{^{'}} (x^{2} + 2) + 4 x (y^{2} + 2 y + 1) = 0

(1 + cos (5 t))^{- 4}

\frac{d}{d x} (\frac{x ^{2} + 2}{x})

\int \frac{- 5 e ^{- 5 x}}{( e ^{- 5 x} + 3 ) ^{3}} d x

s \to 2 - lim (s + ∣ 3 s - 6 ∣)

What is the limit as x approaches 3 of ((x^2-2x-3))/(x^2-9) ?
The limit as x approaches 3 of ((x^2-2x-3))/(x^2-9) is 2/3