Algebra Examples

$f (x) = x^{2} - 4 x + 3$ , $g (x) = x - 3$

Step 1

Replace the function designators with the actual functions in $\frac{f (x)}{g (x)}$ .

$\frac{x^{2} - 4 x + 3}{x - 3}$

Step 2

Simplify.

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Step 2.1

Factor $x^{2} - 4 x + 3$ using the AC method.

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Step 2.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $3$ and whose sum is $- 4$ .

$- 3, - 1$

Step 2.1.2

Write the factored form using these integers.

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

Step 2.2

Cancel the common factor of $x - 3$ .

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Step 2.2.1

Cancel the common factor.

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

Step 2.2.2

Divide $x - 1$ by $1$ .

$x - 1$