Simplify (2x-3)/(x^2-8x+12)-(x-1)/(x^2-8x+12)

$\frac{2 x - 3}{x^{2} - 8 x + 12} - \frac{x - 1}{x^{2} - 8 x + 12}$

Step 1

Simplify terms.

Combine the numerators over the common denominator.

$\frac{2 x - 3 - (x - 1)}{x^{2} - 8 x + 12}$

Simplify each term.

Apply the distributive property.

$\frac{2 x - 3 - x - - 1}{x^{2} - 8 x + 12}$

Multiply $- 1$ by $- 1$ .

$\frac{2 x - 3 - x + 1}{x^{2} - 8 x + 12}$

Simplify by adding terms.

Subtract $x$ from $2 x$ .

$\frac{x - 3 + 1}{x^{2} - 8 x + 12}$

Add $- 3$ and $1$ .

$\frac{x - 2}{x^{2} - 8 x + 12}$

Step 2

Factor $x^{2} - 8 x + 12$ 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 $- 8$ .

$- 6, - 2$

Write the factored form using these integers.

$\frac{x - 2}{(x - 6) (x - 2)}$

Step 3

Cancel the common factor of $x - 2$ .

Cancel the common factor.

$\frac{x - 2}{(x - 6) (x - 2)}$

Rewrite the expression.

$\frac{1}{x - 6}$

Simplify (2x-3)/(x^2-8x+12)-(x-1)/(x^2-8x+12)

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