Calculus Examples

$c x = 1.9 + \frac{1000}{x}$

Step 1

Divide each term in $c x = 1.9 + \frac{1000}{x}$ by $x$ .

$\frac{c x}{x} = \frac{1.9}{x} + \frac{\frac{1000}{x}}{x}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $x$ .

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Step 2.1.1

Cancel the common factor.

$\frac{c x}{x} = \frac{1.9}{x} + \frac{\frac{1000}{x}}{x}$

Step 2.1.2

Divide $c$ by $1$ .

$c = \frac{1.9}{x} + \frac{\frac{1000}{x}}{x}$

Step 3

Simplify the right side.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply the numerator by the reciprocal of the denominator.

$c = \frac{1.9}{x} + \frac{1000}{x} \cdot \frac{1}{x}$

Step 3.1.2

Multiply $\frac{1000}{x} \cdot \frac{1}{x}$ .

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Step 3.1.2.1

Multiply $\frac{1000}{x}$ by $\frac{1}{x}$ .

$c = \frac{1.9}{x} + \frac{1000}{x \cdot x}$

Step 3.1.2.2

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

$c = \frac{1.9}{x} + \frac{1000}{x^{1} x}$

Step 3.1.2.3

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

$c = \frac{1.9}{x} + \frac{1000}{x^{1} x^{1}}$

Step 3.1.2.4

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

$c = \frac{1.9}{x} + \frac{1000}{x^{1 + 1}}$

Step 3.1.2.5

Add $1$ and $1$ .

$c = \frac{1.9}{x} + \frac{1000}{x^{2}}$