Algebra Examples

$\frac{e^{- 0.1} - 1}{- 0.1}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\frac{1}{e^{0.1}} - 1}{- 0.1}$

Step 1.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{e^{0.1}}{e^{0.1}}$ .

$\frac{\frac{1}{e^{0.1}} - 1 \cdot \frac{e^{0.1}}{e^{0.1}}}{- 0.1}$

Step 1.3

Combine $- 1$ and $\frac{e^{0.1}}{e^{0.1}}$ .

$\frac{\frac{1}{e^{0.1}} + \frac{- e^{0.1}}{e^{0.1}}}{- 0.1}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{\frac{1 - e^{0.1}}{e^{0.1}}}{- 0.1}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{1 - e^{0.1}}{e^{0.1}} \cdot \frac{1}{- 0.1}$

Step 3

Divide $1$ by $- 0.1$ .

$\frac{1 - e^{0.1}}{e^{0.1}} \cdot - 10$

Step 4

Combine $\frac{1 - e^{0.1}}{e^{0.1}}$ and $- 10$ .

$\frac{(1 - e^{0.1}) \cdot - 10}{e^{0.1}}$

Step 5

Simplify the expression.

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Step 5.1

Move $- 10$ to the left of $1 - e^{0.1}$ .

$\frac{- 10 \cdot (1 - e^{0.1})}{e^{0.1}}$

Step 5.2

Move the negative in front of the fraction.

$- \frac{10 (1 - e^{0.1})}{e^{0.1}}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{10 (1 - e^{0.1})}{e^{0.1}}$

Decimal Form:

$0.95162581 \dots$