Algebra Examples

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

Step 1

Factor $2 x$ out of $2 x^{2} - 8 x$ .

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Step 1.1

Factor $2 x$ out of $2 x^{2}$ .

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

Step 1.2

Factor $2 x$ out of $- 8 x$ .

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

Step 1.3

Factor $2 x$ out of $2 x (x) + 2 x (- 4)$ .

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

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

Step 2

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

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Step 2.1

Factor $3$ out of $12$ .

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

Step 2.2

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

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

Step 2.3

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

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

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

Step 3

Cancel the common factor of $x - 4$ and $4 - x$ .

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Step 3.1

Factor $- 1$ out of $x$ .

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

Step 3.2

Rewrite $- 4$ as $- 1 (4)$ .

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

Step 3.3

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

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

Step 3.4

Reorder terms.

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

Step 3.5

Cancel the common factor.

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

Step 3.6

Rewrite the expression.

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

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

Step 4

Simplify the expression.

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Step 4.1

Multiply $- 1$ by $2$ .

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

Step 4.2

Move the negative in front of the fraction.

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

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$