Algebra Examples

$\frac{x^{2} - 8 x + 16}{3 x - 12}$

Step 1

Factor using the perfect square rule.

Tap for more steps...

Step 1.1

Rewrite $16$ as $4^{2}$ .

$\frac{x^{2} - 8 x + 4^{2}}{3 x - 12}$

Step 1.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$8 x = 2 \cdot x \cdot 4$

Step 1.3

Rewrite the polynomial.

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

Step 1.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 4$ .

$\frac{{(x - 4)}^{2}}{3 x - 12}$

Step 2

Factor $3$ out of $3 x - 12$ .

Tap for more steps...

Step 2.1

Factor $3$ out of $3 x$ .

$\frac{{(x - 4)}^{2}}{3 (x) - 12}$

Step 2.2

Factor $3$ out of $- 12$ .

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

Step 2.3

Factor $3$ out of $3 x + 3 \cdot - 4$ .

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

Step 3

Cancel the common factor of ${(x - 4)}^{2}$ and $x - 4$ .

Tap for more steps...

Step 3.1

Factor $x - 4$ out of ${(x - 4)}^{2}$ .

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

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $x - 4$ out of $3 (x - 4)$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$\frac{x - 4}{3}$

Step 4

Split the fraction $\frac{x - 4}{3}$ into two fractions.

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

Step 5

Move the negative in front of the fraction.

$\frac{x}{3} - \frac{4}{3}$