Calculus Examples

$\frac{lim_{x \to - 3} x^{2}}{x^{2} - 9} + x - 6$

Step 1

Move the exponent $2$ from $x^{2}$ outside the limit using the Limits Power Rule.

$\frac{{(lim_{x \to - 3} x)}^{2}}{x^{2} - 9} + x - 6$

Step 2

Evaluate the limit of $x$ by plugging in $- 3$ for $x$ .

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

Step 3

Simplify each term.

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Step 3.1

Raise $- 3$ to the power of $2$ .

$\frac{9}{x^{2} - 9} + x - 6$

Step 3.2

Simplify the denominator.

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Step 3.2.1

Rewrite $9$ as $3^{2}$ .

$\frac{9}{x^{2} - 3^{2}} + x - 6$

Step 3.2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

$\frac{9}{(x + 3) (x - 3)} + x - 6$