Algebra Examples

$\frac{5}{- 5 i}$

Step 1

Cancel the common factor of $5$ and $- 5$ .

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Step 1.1

Factor $5$ out of $5$ .

$\frac{5 (1)}{- 5 i}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $5$ out of $- 5 i$ .

$\frac{5 (1)}{5 (- i)}$

Step 1.2.2

Cancel the common factor.

$\frac{5 \cdot 1}{5 (- i)}$

Step 1.2.3

Rewrite the expression.

$\frac{1}{- i}$

Step 2

Cancel the common factor of $1$ and $- 1$ .

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Step 2.1

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- 1 (- 1)}{- i}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{1}{i}$

Step 3

Multiply the numerator and denominator of $\frac{1}{i}$ by the conjugate of $i$ to make the denominator real.

$- (\frac{1}{i} \cdot \frac{i}{i})$

Step 4

Multiply.

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Step 4.1

Combine.

$- \frac{1 i}{i i}$

Step 4.2

Multiply $i$ by $1$ .

$- \frac{i}{i i}$

Step 4.3

Simplify the denominator.

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Step 4.3.1

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

$- \frac{i}{i^{1} i}$

Step 4.3.2

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

$- \frac{i}{i^{1} i^{1}}$

Step 4.3.3

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

$- \frac{i}{i^{1 + 1}}$

Step 4.3.4

Add $1$ and $1$ .

$- \frac{i}{i^{2}}$

Step 4.3.5

Rewrite $i^{2}$ as $- 1$ .

$- \frac{i}{- 1}$

Step 5

Move the negative one from the denominator of $\frac{i}{- 1}$ .

$- (- 1 \cdot i)$

Step 6

Rewrite $- 1 \cdot i$ as $- i$ .

$- - i$

Step 7

Multiply $- 1$ by $- 1$ .

$1 i$

Step 8

Multiply $i$ by $1$ .

$i$