Precalculus Examples

$\frac{- 10 x^{5} + 15 x}{- 5 x}$

Step 1

Factor $5 x$ out of $- 10 x^{5} + 15 x$ .

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Step 1.1

Factor $5 x$ out of $- 10 x^{5}$ .

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

Step 1.2

Factor $5 x$ out of $15 x$ .

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

Step 1.3

Factor $5 x$ out of $5 x (- 2 x^{4}) + 5 x (3)$ .

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

Step 2

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

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Step 2.1

Factor $5$ out of $5 x (- 2 x^{4} + 3)$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{- 2 x^{4} + 3}{- 1}$

Step 3.3

Move the negative one from the denominator of $\frac{- 2 x^{4} + 3}{- 1}$ .

$- 1 \cdot (- 2 x^{4} + 3)$

Step 4

Rewrite $- 1 \cdot (- 2 x^{4} + 3)$ as $- (- 2 x^{4} + 3)$ .

$- (- 2 x^{4} + 3)$

Step 5

Apply the distributive property.

$- (- 2 x^{4}) - 1 \cdot 3$

Step 6

Multiply.

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Step 6.1

Multiply $- 2$ by $- 1$ .

$2 x^{4} - 1 \cdot 3$

Step 6.2

Multiply $- 1$ by $3$ .

$2 x^{4} - 3$