limit x->3 (x^2-9)/(x-3) — step-by-step solution | Explain MAths

limit x->3 (x^2-9)/(x-3)

Let's evaluate the limit of

\frac{x^{2} - 9}{x - 3}

when

x \to 3

The limit of

x^{2}

is

9

when

x \to 3

The limit of

x^{2} - 9

is

0

when

x \to 3

The limit of

x - 3

is

0

when

x \to 3

For

\frac{x^{2} - 9}{x - 3}

, we encounter the indeterminate form 0/0 as

x

tends to

3

To find the limit, we factorize the numerator and the denominator:

x^{2} - 9

Factors identified:

(x + 3) \cdot (x - 3)

Let's reduce:

\frac{(x + 3) \cdot (x - 3)}{x - 3}

x + 3

The limit of

x + 3

is

6

when

x \to 3

So the limit of

\frac{x^{2} - 9}{x - 3}

is

6

when

x \to 3

▷Result: $6$