Calculus Examples

$2 x - \frac{5488}{x^{2}}$

Step 1

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{x^{2}}{x^{2}}$ .

$\frac{2 x \cdot x^{2}}{x^{2}} - \frac{5488}{x^{2}}$

Step 2

Combine the numerators over the common denominator.

$\frac{2 x \cdot x^{2} - 5488}{x^{2}}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $2$ out of $2 x \cdot x^{2} - 5488$ .

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Step 3.1.1

Factor $2$ out of $2 x \cdot x^{2}$ .

$\frac{2 (x \cdot x^{2}) - 5488}{x^{2}}$

Step 3.1.2

Factor $2$ out of $- 5488$ .

$\frac{2 (x \cdot x^{2}) + 2 \cdot - 2744}{x^{2}}$

Step 3.1.3

Factor $2$ out of $2 (x \cdot x^{2}) + 2 \cdot - 2744$ .

$\frac{2 (x \cdot x^{2} - 2744)}{x^{2}}$

Step 3.2

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 3.2.1

Multiply $x$ by $x^{2}$ .

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Step 3.2.1.1

Raise $x$ to the power of $1$ .

$\frac{2 (x^{1} x^{2} - 2744)}{x^{2}}$

Step 3.2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 (x^{1 + 2} - 2744)}{x^{2}}$

Step 3.2.2

Add $1$ and $2$ .

$\frac{2 (x^{3} - 2744)}{x^{2}}$

Step 3.3

Rewrite $2744$ as $14^{3}$ .

$\frac{2 (x^{3} - 14^{3})}{x^{2}}$

Step 3.4

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = x$ and $b = 14$ .

$\frac{2 ((x - 14) (x^{2} + x \cdot 14 + 14^{2}))}{x^{2}}$

Step 3.5

Simplify.

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Step 3.5.1

Move $14$ to the left of $x$ .

$\frac{2 ((x - 14) (x^{2} + 14 \cdot x + 14^{2}))}{x^{2}}$

Step 3.5.2

Raise $14$ to the power of $2$ .

$\frac{2 ((x - 14) (x^{2} + 14 x + 196))}{x^{2}}$

$\frac{2 (x - 14) (x^{2} + 14 x + 196)}{x^{2}}$