Algebra Examples

$\frac{8 x^{8} - 12 x^{6}}{- 4 x^{8}}$

Step 1

Factor $4 x^{6}$ out of $8 x^{8} - 12 x^{6}$ .

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Step 1.1

Factor $4 x^{6}$ out of $8 x^{8}$ .

$\frac{4 x^{6} (2 x^{2}) - 12 x^{6}}{- 4 x^{8}}$

Step 1.2

Factor $4 x^{6}$ out of $- 12 x^{6}$ .

$\frac{4 x^{6} (2 x^{2}) + 4 x^{6} (- 3)}{- 4 x^{8}}$

Step 1.3

Factor $4 x^{6}$ out of $4 x^{6} (2 x^{2}) + 4 x^{6} (- 3)$ .

$\frac{4 x^{6} (2 x^{2} - 3)}{- 4 x^{8}}$

Step 2

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

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Step 2.1

Factor $4$ out of $4 x^{6} (2 x^{2} - 3)$ .

$\frac{4 (x^{6} (2 x^{2} - 3))}{- 4 x^{8}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $- 4 x^{8}$ .

$\frac{4 (x^{6} (2 x^{2} - 3))}{4 (- x^{8})}$

Step 2.2.2

Cancel the common factor.

$\frac{4 (x^{6} (2 x^{2} - 3))}{4 (- x^{8})}$

Step 2.2.3

Rewrite the expression.

$\frac{x^{6} (2 x^{2} - 3)}{- x^{8}}$

Step 3

Cancel the common factors.

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Step 3.1

Factor $x^{6}$ out of $- x^{8}$ .

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

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

Step 4

Move the negative in front of the fraction.

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

Step 5

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

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

Step 6

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

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Step 6.1

Cancel the common factor.

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

Step 6.2

Divide $2$ by $1$ .

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

Step 7

Move the negative in front of the fraction.

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