Pre-Algebra Examples

$\frac{15 u^{2} v^{6} - 10 u^{6} y^{6}}{20 u^{3}}$

Step 1

Factor $5 u^{2}$ out of $15 u^{2} v^{6} - 10 u^{6} y^{6}$ .

Tap for more steps...

Step 1.1

Factor $5 u^{2}$ out of $15 u^{2} v^{6}$ .

$\frac{5 u^{2} (3 v^{6}) - 10 u^{6} y^{6}}{20 u^{3}}$

Step 1.2

Factor $5 u^{2}$ out of $- 10 u^{6} y^{6}$ .

$\frac{5 u^{2} (3 v^{6}) + 5 u^{2} (- 2 u^{4} y^{6})}{20 u^{3}}$

Step 1.3

Factor $5 u^{2}$ out of $5 u^{2} (3 v^{6}) + 5 u^{2} (- 2 u^{4} y^{6})$ .

$\frac{5 u^{2} (3 v^{6} - 2 u^{4} y^{6})}{20 u^{3}}$

Step 2

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

Tap for more steps...

Step 2.1

Factor $5$ out of $5 u^{2} (3 v^{6} - 2 u^{4} y^{6})$ .

$\frac{5 (u^{2} (3 v^{6} - 2 u^{4} y^{6}))}{20 u^{3}}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $5$ out of $20 u^{3}$ .

$\frac{5 (u^{2} (3 v^{6} - 2 u^{4} y^{6}))}{5 (4 u^{3})}$

Step 2.2.2

Cancel the common factor.

$\frac{5 (u^{2} (3 v^{6} - 2 u^{4} y^{6}))}{5 (4 u^{3})}$

Step 2.2.3

Rewrite the expression.

$\frac{u^{2} (3 v^{6} - 2 u^{4} y^{6})}{4 u^{3}}$

Step 3

Cancel the common factors.

Tap for more steps...

Step 3.1

Factor $u^{2}$ out of $4 u^{3}$ .

$\frac{u^{2} (3 v^{6} - 2 u^{4} y^{6})}{u^{2} (4 u)}$

Step 3.2

Cancel the common factor.

$\frac{u^{2} (3 v^{6} - 2 u^{4} y^{6})}{u^{2} (4 u)}$

Step 3.3

Rewrite the expression.

$\frac{3 v^{6} - 2 u^{4} y^{6}}{4 u}$

Step 4

Split the fraction $\frac{3 v^{6} - 2 u^{4} y^{6}}{4 u}$ into two fractions.

$\frac{3 v^{6}}{4 u} + \frac{- 2 u^{4} y^{6}}{4 u}$

Step 5

Cancel the common factor of $- 2$ and $4$ .

Tap for more steps...

Step 5.1

Factor $2$ out of $- 2 u^{4} y^{6}$ .

$\frac{3 v^{6}}{4 u} + \frac{2 (- u^{4} y^{6})}{4 u}$

Step 5.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1

Factor $2$ out of $4 u$ .

$\frac{3 v^{6}}{4 u} + \frac{2 (- u^{4} y^{6})}{2 (2 u)}$

Step 5.2.2

Cancel the common factor.

$\frac{3 v^{6}}{4 u} + \frac{2 (- u^{4} y^{6})}{2 (2 u)}$

Step 5.2.3

Rewrite the expression.

$\frac{3 v^{6}}{4 u} + \frac{- u^{4} y^{6}}{2 u}$

Step 6

Cancel the common factor of $u^{4}$ and $u$ .

Tap for more steps...

Step 6.1

Factor $u$ out of $- u^{4} y^{6}$ .

$\frac{3 v^{6}}{4 u} + \frac{u (- u^{3} y^{6})}{2 u}$

Step 6.2

Cancel the common factors.

Tap for more steps...

Step 6.2.1

Factor $u$ out of $2 u$ .

$\frac{3 v^{6}}{4 u} + \frac{u (- u^{3} y^{6})}{u \cdot 2}$

Step 6.2.2

Cancel the common factor.

$\frac{3 v^{6}}{4 u} + \frac{u (- u^{3} y^{6})}{u \cdot 2}$

Step 6.2.3

Rewrite the expression.

$\frac{3 v^{6}}{4 u} + \frac{- u^{3} y^{6}}{2}$

Step 7

Move the negative in front of the fraction.

$\frac{3 v^{6}}{4 u} - \frac{u^{3} y^{6}}{2}$