What is the limit as x approaches 3 of (4x^2-36)/(2x-6) ?

The limit as x approaches 3 of (4x^2-36)/(2x-6) is 12

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limit as x approaches 3 of (4x^2-36)/(2x-6)

x \to 3 lim (\frac{4 x ^{2} - 36}{2 x - 6})

12

Solution steps

x \to 3 lim (\frac{4 x ^{2} - 36}{2 x - 6})

Simplify

\frac{4 x ^{2} - 36}{2 x - 6} : 2 (x + 3)

= x \to 3 lim (2 (x + 3))

Plug in the value

x = 3

= 2 (3 + 3)

Simplify

= 12

What is the limit as x approaches 3 of (4x^2-36)/(2x-6) ?
The limit as x approaches 3 of (4x^2-36)/(2x-6) is 12