Evaluate the Function f(x)=(x^2-6x+9)/(x-3) , a=3

$f (x) = \frac{x^{2} - 6 x + 9}{x - 3}$ , $a = 3$

Step 1

Replace the variable $a$ with $3$ in the expression.

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

Step 2

Simplify the result.

Factor using the perfect square rule.

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

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

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$6 x = 2 \cdot x \cdot 3$

Rewrite the polynomial.

$f (x) = \frac{x^{2} - 2 \cdot x \cdot 3 + 3^{2}}{x - 3}$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 3$ .

$f (x) = \frac{{(x - 3)}^{2}}{x - 3}$

Cancel the common factor of ${(x - 3)}^{2}$ and $x - 3$ .

Factor $x - 3$ out of ${(x - 3)}^{2}$ .

$f (x) = \frac{(x - 3) (x - 3)}{x - 3}$

Cancel the common factors.

Multiply by $1$ .

$f (x) = \frac{(x - 3) (x - 3)}{(x - 3) \cdot 1}$

Cancel the common factor.

$f (x) = \frac{(x - 3) (x - 3)}{(x - 3) \cdot 1}$

Rewrite the expression.

$f (x) = \frac{x - 3}{1}$

Divide $x - 3$ by $1$ .

$f (x) = x - 3$

The final answer is $x - 3$ .

$x - 3$

Step 3