Algebra Examples

$\frac{12 x^{3} (5 - 2 x)}{18 x (2 x - 5)}$

Step 1

Cancel the common factor of $12$ and $18$ .

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Step 1.1

Factor $6$ out of $12 x^{3} (5 - 2 x)$ .

$\frac{6 (2 x^{3} (5 - 2 x))}{18 x (2 x - 5)}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $6$ out of $18 x (2 x - 5)$ .

$\frac{6 (2 x^{3} (5 - 2 x))}{6 (3 x (2 x - 5))}$

Step 1.2.2

Cancel the common factor.

$\frac{6 (2 x^{3} (5 - 2 x))}{6 (3 x (2 x - 5))}$

Step 1.2.3

Rewrite the expression.

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

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

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

Step 2

Cancel the common factor of $x^{3}$ and $x$ .

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Step 2.1

Factor $x$ out of $2 x^{3} (5 - 2 x)$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $x$ out of $3 x (2 x - 5)$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

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

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

Step 3

Cancel the common factor of $5 - 2 x$ and $2 x - 5$ .

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Step 3.1

Rewrite $5$ as $- 1 (- 5)$ .

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

Step 3.2

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

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

Step 3.3

Factor $- 1$ out of $- 1 (- 5) - (2 x)$ .

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

Step 3.4

Reorder terms.

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

Step 3.5

Cancel the common factor.

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

Step 3.6

Rewrite the expression.

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

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

Step 4

Simplify the expression.

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Step 4.1

Multiply $- 1$ by $2$ .

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

Step 4.2

Move the negative in front of the fraction.

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

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

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