Simplify (x^2-7x+12)/(x^2-4x+3)

$\frac{x^{2} - 7 x + 12}{x^{2} - 4 x + 3}$

Step 1

Factor $x^{2} - 7 x + 12$ using the AC method.

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 $12$ and whose sum is $- 7$ .

$- 4, - 3$

Write the factored form using these integers.

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

Step 2

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

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 $- 4$ .

$- 3, - 1$

Write the factored form using these integers.

$\frac{(x - 4) (x - 3)}{(x - 3) (x - 1)}$

Step 3

Cancel the common factor of $x - 3$ .

Cancel the common factor.

$\frac{(x - 4) (x - 3)}{(x - 3) (x - 1)}$

Rewrite the expression.

$\frac{x - 4}{x - 1}$

Simplify (x^2-7x+12)/(x^2-4x+3)

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