Precalculus Examples

$\frac{3 x^{3} - 8 i x^{2} + 2 x + (1 - 3 i)}{x - 2 i}$

Step 1

Remove parentheses.

$\frac{3 x^{3} - 8 i x^{2} + 2 x + 1 - 3 i}{x - 2 i}$

Step 2

Split the fraction $\frac{3 x^{3} - 8 i x^{2} + 2 x + 1 - 3 i}{x - 2 i}$ into two fractions.

$\frac{3 x^{3} - 8 i x^{2} + 2 x + 1}{x - 2 i} + \frac{- 3 i}{x - 2 i}$

Step 3

Split the fraction $\frac{3 x^{3} - 8 i x^{2} + 2 x + 1}{x - 2 i}$ into two fractions.

$\frac{3 x^{3} - 8 i x^{2} + 2 x}{x - 2 i} + \frac{1}{x - 2 i} + \frac{- 3 i}{x - 2 i}$

Step 4

Split the fraction $\frac{3 x^{3} - 8 i x^{2} + 2 x}{x - 2 i}$ into two fractions.

$\frac{3 x^{3} - 8 i x^{2}}{x - 2 i} + \frac{2 x}{x - 2 i} + \frac{1}{x - 2 i} + \frac{- 3 i}{x - 2 i}$

Step 5

Split the fraction $\frac{3 x^{3} - 8 i x^{2}}{x - 2 i}$ into two fractions.

$\frac{3 x^{3}}{x - 2 i} + \frac{- 8 i x^{2}}{x - 2 i} + \frac{2 x}{x - 2 i} + \frac{1}{x - 2 i} + \frac{- 3 i}{x - 2 i}$

Step 6

Move the negative in front of the fraction.

$\frac{3 x^{3}}{x - 2 i} - \frac{8 i x^{2}}{x - 2 i} + \frac{2 x}{x - 2 i} + \frac{1}{x - 2 i} + \frac{- 3 i}{x - 2 i}$

Step 7

Move the negative in front of the fraction.

$\frac{3 x^{3}}{x - 2 i} - \frac{8 i x^{2}}{x - 2 i} + \frac{2 x}{x - 2 i} + \frac{1}{x - 2 i} - \frac{3 i}{x - 2 i}$