Finite Math Examples

$\frac{e^{3 x} d}{d x} + 3 e^{3 x} y$

Step 1

Cancel the common factor of $d$ .

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Step 1.1

Cancel the common factor.

$\frac{e^{3 x} d}{d x} + 3 e^{3 x} y$

Step 1.2

Rewrite the expression.

$\frac{e^{3 x}}{x} + 3 e^{3 x} y$

Step 2

To write $3 e^{3 x} y$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{e^{3 x}}{x} + \frac{3 e^{3 x} y x}{x}$

Step 3

Combine the numerators over the common denominator.

$\frac{e^{3 x} + 3 e^{3 x} y x}{x}$

Step 4

Factor $e^{3 x}$ out of $e^{3 x} + 3 e^{3 x} y x$ .

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Step 4.1

Multiply by $1$ .

$\frac{e^{3 x} \cdot 1 + 3 e^{3 x} y x}{x}$

Step 4.2

Factor $e^{3 x}$ out of $3 e^{3 x} y x$ .

$\frac{e^{3 x} \cdot 1 + e^{3 x} (3 y x)}{x}$

Step 4.3

Factor $e^{3 x}$ out of $e^{3 x} \cdot 1 + e^{3 x} (3 y x)$ .

$\frac{e^{3 x} (1 + 3 y x)}{x}$