Pre-Algebra Examples

$\frac{17 u^{7} x^{5} - 15 u^{7} x^{2}}{- 3 u^{5} x^{3}}$

Step 1

Factor $u^{7} x^{2}$ out of $17 u^{7} x^{5} - 15 u^{7} x^{2}$ .

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Step 1.1

Factor $u^{7} x^{2}$ out of $17 u^{7} x^{5}$ .

$\frac{u^{7} x^{2} (17 x^{3}) - 15 u^{7} x^{2}}{- 3 u^{5} x^{3}}$

Step 1.2

Factor $u^{7} x^{2}$ out of $- 15 u^{7} x^{2}$ .

$\frac{u^{7} x^{2} (17 x^{3}) + u^{7} x^{2} (- 15)}{- 3 u^{5} x^{3}}$

Step 1.3

Factor $u^{7} x^{2}$ out of $u^{7} x^{2} (17 x^{3}) + u^{7} x^{2} (- 15)$ .

$\frac{u^{7} x^{2} (17 x^{3} - 15)}{- 3 u^{5} x^{3}}$

Step 2

Cancel the common factor of $u^{7}$ and $u^{5}$ .

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Step 2.1

Factor $u^{5}$ out of $u^{7} x^{2} (17 x^{3} - 15)$ .

$\frac{u^{5} (u^{2} x^{2} (17 x^{3} - 15))}{- 3 u^{5} x^{3}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $u^{5}$ out of $- 3 u^{5} x^{3}$ .

$\frac{u^{5} (u^{2} x^{2} (17 x^{3} - 15))}{u^{5} (- 3 x^{3})}$

Step 2.2.2

Cancel the common factor.

$\frac{u^{5} (u^{2} x^{2} (17 x^{3} - 15))}{u^{5} (- 3 x^{3})}$

Step 2.2.3

Rewrite the expression.

$\frac{u^{2} x^{2} (17 x^{3} - 15)}{- 3 x^{3}}$

Step 3

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

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Step 3.1

Factor $x^{2}$ out of $u^{2} x^{2} (17 x^{3} - 15)$ .

$\frac{x^{2} (u^{2} (17 x^{3} - 15))}{- 3 x^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{x^{2} (u^{2} (17 x^{3} - 15))}{x^{2} (- 3 x)}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{2} (u^{2} (17 x^{3} - 15))}{x^{2} (- 3 x)}$

Step 3.2.3

Rewrite the expression.

$\frac{u^{2} (17 x^{3} - 15)}{- 3 x}$

Step 4

Move the negative in front of the fraction.

$- \frac{u^{2} (17 x^{3} - 15)}{3 x}$

Step 5

Apply the distributive property.

$- \frac{u^{2} (17 x^{3}) + u^{2} \cdot - 15}{3 x}$

Step 6

Rewrite using the commutative property of multiplication.

$- \frac{17 u^{2} x^{3} + u^{2} \cdot - 15}{3 x}$

Step 7

Move $- 15$ to the left of $u^{2}$ .

$- \frac{17 u^{2} x^{3} - 15 u^{2}}{3 x}$

Step 8

Split the fraction $\frac{17 u^{2} x^{3} - 15 u^{2}}{3 x}$ into two fractions.

$- (\frac{17 u^{2} x^{3}}{3 x} + \frac{- 15 u^{2}}{3 x})$

Step 9

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

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Step 9.1

Factor $x$ out of $17 u^{2} x^{3}$ .

$- (\frac{x (17 u^{2} x^{2})}{3 x} + \frac{- 15 u^{2}}{3 x})$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $x$ out of $3 x$ .

$- (\frac{x (17 u^{2} x^{2})}{x \cdot 3} + \frac{- 15 u^{2}}{3 x})$

Step 9.2.2

Cancel the common factor.

$- (\frac{x (17 u^{2} x^{2})}{x \cdot 3} + \frac{- 15 u^{2}}{3 x})$

Step 9.2.3

Rewrite the expression.

$- (\frac{17 u^{2} x^{2}}{3} + \frac{- 15 u^{2}}{3 x})$

Step 10

Cancel the common factor of $- 15$ and $3$ .

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Step 10.1

Factor $3$ out of $- 15 u^{2}$ .

$- (\frac{17 u^{2} x^{2}}{3} + \frac{3 (- 5 u^{2})}{3 x})$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $3$ out of $3 x$ .

$- (\frac{17 u^{2} x^{2}}{3} + \frac{3 (- 5 u^{2})}{3 (x)})$

Step 10.2.2

Cancel the common factor.

$- (\frac{17 u^{2} x^{2}}{3} + \frac{3 (- 5 u^{2})}{3 x})$

Step 10.2.3

Rewrite the expression.

$- (\frac{17 u^{2} x^{2}}{3} + \frac{- 5 u^{2}}{x})$

Step 11

Move the negative in front of the fraction.

$- (\frac{17 u^{2} x^{2}}{3} - \frac{5 u^{2}}{x})$