What is the limit as x approaches 3 of (x^3-9x)/(3x^2-6x-9) ?

The limit as x approaches 3 of (x^3-9x)/(3x^2-6x-9) is 3/2

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limit as x approaches 3 of (x^3-9x)/(3x^2-6x-9)

x \to 3 lim (\frac{x ^{3} - 9 x}{3 x ^{2} - 6 x - 9})

\frac{3}{2}

Decimal

1.5

Solution steps

x \to 3 lim (\frac{x ^{3} - 9 x}{3 x ^{2} - 6 x - 9})

Simplify

\frac{x ^{3} - 9 x}{3 x ^{2} - 6 x - 9} : \frac{x ( x + 3 )}{3 ( x + 1 )}

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

Plug in the value

x = 3

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

Simplify

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

= \frac{3}{2}

What is the limit as x approaches 3 of (x^3-9x)/(3x^2-6x-9) ?
The limit as x approaches 3 of (x^3-9x)/(3x^2-6x-9) is 3/2