Finite Math Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

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

Tap for more steps...

Step 2.1

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 $2$ and whose sum is $- 3$ .

$- 2, - 1$

Step 2.2

Write the factored form using these integers.

$\frac{(x - 2) (x - 1)}{x + 2} \cdot \frac{x - 3}{3 x - 3}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Factor $3$ out of $3 x - 3$ .

Tap for more steps...

Step 3.1.1

Factor $3$ out of $3 x$ .

$\frac{(x - 2) (x - 1)}{x + 2} \cdot \frac{x - 3}{3 (x) - 3}$

Step 3.1.2

Factor $3$ out of $- 3$ .

$\frac{(x - 2) (x - 1)}{x + 2} \cdot \frac{x - 3}{3 (x) + 3 (- 1)}$

Step 3.1.3

Factor $3$ out of $3 (x) + 3 (- 1)$ .

$\frac{(x - 2) (x - 1)}{x + 2} \cdot \frac{x - 3}{3 (x - 1)}$

Step 3.2

Cancel the common factor of $x - 1$ .

Tap for more steps...

Step 3.2.1

Factor $x - 1$ out of $(x - 2) (x - 1)$ .

$\frac{(x - 1) (x - 2)}{x + 2} \cdot \frac{x - 3}{3 (x - 1)}$

Step 3.2.2

Factor $x - 1$ out of $3 (x - 1)$ .

$\frac{(x - 1) (x - 2)}{x + 2} \cdot \frac{x - 3}{(x - 1) \cdot 3}$

Step 3.2.3

Cancel the common factor.

$\frac{(x - 1) (x - 2)}{x + 2} \cdot \frac{x - 3}{(x - 1) \cdot 3}$

Step 3.2.4

Rewrite the expression.

$\frac{x - 2}{x + 2} \cdot \frac{x - 3}{3}$

Step 3.3

Multiply $\frac{x - 2}{x + 2}$ by $\frac{x - 3}{3}$ .

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

Step 3.4

Move $3$ to the left of $x + 2$ .

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