Pre-Algebra Examples

$\frac{6 x^{2} - 3 x}{10 x^{3} + 50 x^{2}}$

Step 1

Factor $3 x$ out of $6 x^{2} - 3 x$ .

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Step 1.1

Factor $3 x$ out of $6 x^{2}$ .

$\frac{3 x (2 x) - 3 x}{10 x^{3} + 50 x^{2}}$

Step 1.2

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

$\frac{3 x (2 x) + 3 x (- 1)}{10 x^{3} + 50 x^{2}}$

Step 1.3

Factor $3 x$ out of $3 x (2 x) + 3 x (- 1)$ .

$\frac{3 x (2 x - 1)}{10 x^{3} + 50 x^{2}}$

Step 2

Factor $10 x^{2}$ out of $10 x^{3} + 50 x^{2}$ .

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Step 2.1

Factor $10 x^{2}$ out of $10 x^{3}$ .

$\frac{3 x (2 x - 1)}{10 x^{2} (x) + 50 x^{2}}$

Step 2.2

Factor $10 x^{2}$ out of $50 x^{2}$ .

$\frac{3 x (2 x - 1)}{10 x^{2} (x) + 10 x^{2} (5)}$

Step 2.3

Factor $10 x^{2}$ out of $10 x^{2} (x) + 10 x^{2} (5)$ .

$\frac{3 x (2 x - 1)}{10 x^{2} (x + 5)}$

Step 3

Cancel the common factor of $x$ and $x^{2}$ .

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Step 3.1

Factor $x$ out of $3 x (2 x - 1)$ .

$\frac{x (3 (2 x - 1))}{10 x^{2} (x + 5)}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x$ out of $10 x^{2} (x + 5)$ .

$\frac{x (3 (2 x - 1))}{x (10 x (x + 5))}$

Step 3.2.2

Cancel the common factor.

$\frac{x (3 (2 x - 1))}{x (10 x (x + 5))}$

Step 3.2.3

Rewrite the expression.

$\frac{3 (2 x - 1)}{10 x (x + 5)}$