Simplify 5/(2e^2)-15/(4e)

$\frac{5}{2 e^{2}} - \frac{15}{4 e}$

Step 1

To write $\frac{5}{2 e^{2}}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{2 e^{2}} \cdot \frac{2}{2} - \frac{15}{4 e}$

Step 2

To write $- \frac{15}{4 e}$ as a fraction with a common denominator, multiply by $\frac{e}{e}$ .

$\frac{5}{2 e^{2}} \cdot \frac{2}{2} - \frac{15}{4 e} \cdot \frac{e}{e}$

Step 3

Write each expression with a common denominator of $4 e^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{2 e^{2}}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 2}{2 e^{2} \cdot 2} - \frac{15}{4 e} \cdot \frac{e}{e}$

Multiply $2$ by $2$ .

$\frac{5 \cdot 2}{4 e^{2}} - \frac{15}{4 e} \cdot \frac{e}{e}$

Multiply $\frac{15}{4 e}$ by $\frac{e}{e}$ .

$\frac{5 \cdot 2}{4 e^{2}} - \frac{15 e}{4 e e}$

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

$\frac{5 \cdot 2}{4 e^{2}} - \frac{15 e}{4 (e^{1} e)}$

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

$\frac{5 \cdot 2}{4 e^{2}} - \frac{15 e}{4 (e^{1} e^{1})}$

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

$\frac{5 \cdot 2}{4 e^{2}} - \frac{15 e}{4 e^{1 + 1}}$

Add $1$ and $1$ .

$\frac{5 \cdot 2}{4 e^{2}} - \frac{15 e}{4 e^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \cdot 2 - 15 e}{4 e^{2}}$

Step 5

Multiply $5$ by $2$ .

$\frac{10 - 15 e}{4 e^{2}}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{10 - 15 e}{4 e^{2}}$

Decimal Form:

$- 1.04120969 \dots$