Pre-Algebra Examples

$\frac{- 40 x^{7} + 90 x^{8}}{15 x^{8}}$

Step 1

Factor $10 x^{7}$ out of $- 40 x^{7} + 90 x^{8}$ .

Tap for more steps...

Step 1.1

Factor $10 x^{7}$ out of $- 40 x^{7}$ .

$\frac{10 x^{7} (- 4) + 90 x^{8}}{15 x^{8}}$

Step 1.2

Factor $10 x^{7}$ out of $90 x^{8}$ .

$\frac{10 x^{7} (- 4) + 10 x^{7} (9 x)}{15 x^{8}}$

Step 1.3

Factor $10 x^{7}$ out of $10 x^{7} (- 4) + 10 x^{7} (9 x)$ .

$\frac{10 x^{7} (- 4 + 9 x)}{15 x^{8}}$

$\frac{10 x^{7} (- 4 + 9 x)}{15 x^{8}}$

Step 2

Cancel the common factor of $10$ and $15$ .

Tap for more steps...

Step 2.1

Factor $5$ out of $10 x^{7} (- 4 + 9 x)$ .

$\frac{5 (2 x^{7} (- 4 + 9 x))}{15 x^{8}}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $5$ out of $15 x^{8}$ .

$\frac{5 (2 x^{7} (- 4 + 9 x))}{5 (3 x^{8})}$

Step 2.2.2

Cancel the common factor.

$\frac{5 (2 x^{7} (- 4 + 9 x))}{5 (3 x^{8})}$

Step 2.2.3

Rewrite the expression.

$\frac{2 x^{7} (- 4 + 9 x)}{3 x^{8}}$

$\frac{2 x^{7} (- 4 + 9 x)}{3 x^{8}}$

$\frac{2 x^{7} (- 4 + 9 x)}{3 x^{8}}$

Step 3

Cancel the common factor of $x^{7}$ and $x^{8}$ .

Tap for more steps...

Step 3.1

Factor $x^{7}$ out of $2 x^{7} (- 4 + 9 x)$ .

$\frac{x^{7} (2 (- 4 + 9 x))}{3 x^{8}}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $x^{7}$ out of $3 x^{8}$ .

$\frac{x^{7} (2 (- 4 + 9 x))}{x^{7} (3 x)}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{7} (2 (- 4 + 9 x))}{x^{7} (3 x)}$

Step 3.2.3

Rewrite the expression.

$\frac{2 (- 4 + 9 x)}{3 x}$

$\frac{2 (- 4 + 9 x)}{3 x}$

$\frac{2 (- 4 + 9 x)}{3 x}$

Step 4

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

$\frac{2 (- 1 (4) + 9 x)}{3 x}$

Step 5

Factor $- 1$ out of $9 x$ .

$\frac{2 (- 1 (4) - (- 9 x))}{3 x}$

Step 6

Factor $- 1$ out of $- 1 (4) - (- 9 x)$ .

$\frac{2 (- 1 (4 - 9 x))}{3 x}$

Step 7

Move the negative in front of the fraction.

$- \frac{2 (4 - 9 x)}{3 x}$

Step 8

Apply the distributive property.

$- \frac{2 \cdot 4 + 2 (- 9 x)}{3 x}$

Step 9

Multiply $2$ by $4$ .

$- \frac{8 + 2 (- 9 x)}{3 x}$

Step 10

Multiply $- 9$ by $2$ .

$- \frac{8 - 18 x}{3 x}$

Step 11

Split the fraction $\frac{8 - 18 x}{3 x}$ into two fractions.

$- (\frac{8}{3 x} + \frac{- 18 x}{3 x})$

Step 12

Cancel the common factor of $- 18$ and $3$ .

Tap for more steps...

Step 12.1

Factor $3$ out of $- 18 x$ .

$- (\frac{8}{3 x} + \frac{3 (- 6 x)}{3 x})$

Step 12.2

Cancel the common factors.

Tap for more steps...

Step 12.2.1

Factor $3$ out of $3 x$ .

$- (\frac{8}{3 x} + \frac{3 (- 6 x)}{3 (x)})$

Step 12.2.2

Cancel the common factor.

$- (\frac{8}{3 x} + \frac{3 (- 6 x)}{3 x})$

Step 12.2.3

Rewrite the expression.

$- (\frac{8}{3 x} + \frac{- 6 x}{x})$

$- (\frac{8}{3 x} + \frac{- 6 x}{x})$

$- (\frac{8}{3 x} + \frac{- 6 x}{x})$

Step 13

Cancel the common factor of $x$ .

Tap for more steps...

Step 13.1

Cancel the common factor.

$- (\frac{8}{3 x} + \frac{- 6 x}{x})$

Step 13.2

Divide $- 6$ by $1$ .

$- (\frac{8}{3 x} - 6)$

$- (\frac{8}{3 x} - 6)$

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