Pre-Algebra Examples

$\frac{12 x^{3} - 24 x^{2}}{5 x - 10}$

Step 1

Write $\frac{12 x^{3} - 24 x^{2}}{5 x - 10}$ as an equation.

$y = \frac{12 x^{3} - 24 x^{2}}{5 x - 10}$

Step 2

Simplify $\frac{12 x^{3} - 24 x^{2}}{5 x - 10}$ .

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Step 2.1

Factor $12 x^{2}$ out of $12 x^{3} - 24 x^{2}$ .

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Step 2.1.1

Factor $12 x^{2}$ out of $12 x^{3}$ .

$y = \frac{12 x^{2} (x) - 24 x^{2}}{5 x - 10}$

Step 2.1.2

Factor $12 x^{2}$ out of $- 24 x^{2}$ .

$y = \frac{12 x^{2} (x) + 12 x^{2} (- 2)}{5 x - 10}$

Step 2.1.3

Factor $12 x^{2}$ out of $12 x^{2} (x) + 12 x^{2} (- 2)$ .

$y = \frac{12 x^{2} (x - 2)}{5 x - 10}$

Step 2.2

Factor $5$ out of $5 x - 10$ .

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Step 2.2.1

Factor $5$ out of $5 x$ .

$y = \frac{12 x^{2} (x - 2)}{5 (x) - 10}$

Step 2.2.2

Factor $5$ out of $- 10$ .

$y = \frac{12 x^{2} (x - 2)}{5 x + 5 \cdot - 2}$

Step 2.2.3

Factor $5$ out of $5 x + 5 \cdot - 2$ .

$y = \frac{12 x^{2} (x - 2)}{5 (x - 2)}$

Step 2.3

Cancel the common factor of $x - 2$ .

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Step 2.3.1

Cancel the common factor.

$y = \frac{12 x^{2} (x - 2)}{5 (x - 2)}$

Step 2.3.2

Rewrite the expression.

$y = \frac{12 x^{2}}{5}$

Step 3

Since the equation can be written in the form $y = k x^{2}$ , $y$ varies directly with $x^{2}$ and $k$ . The constant of variation, $k$ , is $\frac{12}{5}$ .

$\frac{12}{5}$