Simplify 6/(-4i)

$\frac{6}{- 4 i}$

Cancel the common factor of $6$ and $- 4$ .

Factor $2$ out of $6$ .

$\frac{2 (3)}{- 4 i}$

Cancel the common factors.

Factor $2$ out of $- 4 i$ .

$\frac{2 (3)}{2 (- 2 i)}$

Cancel the common factor.

$\frac{2 \cdot 3}{2 (- 2 i)}$

Rewrite the expression.

$\frac{3}{- 2 i}$

Multiply the numerator and denominator of $\frac{3}{- 2 i}$ by the conjugate of $- 2 i$ to make the denominator real.

$\frac{3}{- 2 i} \cdot \frac{i}{i}$

Multiply.

Combine.

$\frac{3 i}{- 2 i i}$

Simplify the denominator.

Add parentheses.

$\frac{3 i}{- 2 (i i)}$

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

$\frac{3 i}{- 2 (i^{1} i)}$

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

$\frac{3 i}{- 2 (i^{1} i^{1})}$

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

$\frac{3 i}{- 2 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{3 i}{- 2 i^{2}}$

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

$\frac{3 i}{- 2 \cdot - 1}$

Multiply $- 2$ by $- 1$ .

$\frac{3 i}{2}$