Pre-Algebra Examples

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

Step 1

Factor $4$ out of $4 x - 4$ .

Tap for more steps...

Step 1.1

Factor $4$ out of $4 x$ .

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

Step 1.2

Factor $4$ out of $- 4$ .

$\frac{x - 3}{4 (x) + 4 (- 1)} \cdot \frac{x^{2} - 3 x + 2}{x + 2}$

Step 1.3

Factor $4$ out of $4 (x) + 4 (- 1)$ .

$\frac{x - 3}{4 (x - 1)} \cdot \frac{x^{2} - 3 x + 2}{x + 2}$

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.

$\frac{x - 3}{4 (x - 1)} \cdot \frac{(x - 2) (x - 1)}{x + 2}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Cancel the common factor of $x - 1$ .

Tap for more steps...

Step 3.1.1

Factor $x - 1$ out of $4 (x - 1)$ .

$\frac{x - 3}{(x - 1) \cdot 4} \cdot \frac{(x - 2) (x - 1)}{x + 2}$

Step 3.1.2

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

$\frac{x - 3}{(x - 1) \cdot 4} \cdot \frac{(x - 1) (x - 2)}{x + 2}$

Step 3.1.3

Cancel the common factor.

$\frac{x - 3}{(x - 1) \cdot 4} \cdot \frac{(x - 1) (x - 2)}{x + 2}$

Step 3.1.4

Rewrite the expression.

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

Step 3.2

Multiply $\frac{x - 3}{4}$ by $\frac{x - 2}{x + 2}$ .

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