Pre-Algebra Examples

$\frac{- 30 x^{2} + 100 x^{3}}{25 x^{3}}$

Step 1

Factor $10 x^{2}$ out of $- 30 x^{2} + 100 x^{3}$ .

Tap for more steps...

Step 1.1

Factor $10 x^{2}$ out of $- 30 x^{2}$ .

$\frac{10 x^{2} (- 3) + 100 x^{3}}{25 x^{3}}$

Step 1.2

Factor $10 x^{2}$ out of $100 x^{3}$ .

$\frac{10 x^{2} (- 3) + 10 x^{2} (10 x)}{25 x^{3}}$

Step 1.3

Factor $10 x^{2}$ out of $10 x^{2} (- 3) + 10 x^{2} (10 x)$ .

$\frac{10 x^{2} (- 3 + 10 x)}{25 x^{3}}$

$\frac{10 x^{2} (- 3 + 10 x)}{25 x^{3}}$

Step 2

Cancel the common factor of $10$ and $25$ .

Tap for more steps...

Step 2.1

Factor $5$ out of $10 x^{2} (- 3 + 10 x)$ .

$\frac{5 (2 x^{2} (- 3 + 10 x))}{25 x^{3}}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $5$ out of $25 x^{3}$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

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

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

Step 3

Cancel the common factor of $x^{2}$ and $x^{3}$ .

Tap for more steps...

Step 3.1

Factor $x^{2}$ out of $2 x^{2} (- 3 + 10 x)$ .

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

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

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

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

Step 4

Rewrite $- 3$ as $- 1 (3)$ .

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

Step 5

Factor $- 1$ out of $10 x$ .

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

Step 6

Factor $- 1$ out of $- 1 (3) - (- 10 x)$ .

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

Step 7

Move the negative in front of the fraction.

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

Step 8

Apply the distributive property.

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

Step 9

Multiply $2$ by $3$ .

$- \frac{6 + 2 (- 10 x)}{5 x}$

Step 10

Multiply $- 10$ by $2$ .

$- \frac{6 - 20 x}{5 x}$

Step 11

Split the fraction $\frac{6 - 20 x}{5 x}$ into two fractions.

$- (\frac{6}{5 x} + \frac{- 20 x}{5 x})$

Step 12

Cancel the common factor of $- 20$ and $5$ .

Tap for more steps...

Step 12.1

Factor $5$ out of $- 20 x$ .

$- (\frac{6}{5 x} + \frac{5 (- 4 x)}{5 x})$

Step 12.2

Cancel the common factors.

Tap for more steps...

Step 12.2.1

Factor $5$ out of $5 x$ .

$- (\frac{6}{5 x} + \frac{5 (- 4 x)}{5 (x)})$

Step 12.2.2

Cancel the common factor.

$- (\frac{6}{5 x} + \frac{5 (- 4 x)}{5 x})$

Step 12.2.3

Rewrite the expression.

$- (\frac{6}{5 x} + \frac{- 4 x}{x})$

$- (\frac{6}{5 x} + \frac{- 4 x}{x})$

$- (\frac{6}{5 x} + \frac{- 4 x}{x})$

Step 13

Cancel the common factor of $x$ .

Tap for more steps...

Step 13.1

Cancel the common factor.

$- (\frac{6}{5 x} + \frac{- 4 x}{x})$

Step 13.2

Divide $- 4$ by $1$ .

$- (\frac{6}{5 x} - 4)$

$- (\frac{6}{5 x} - 4)$

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