Precalculus Examples

$\frac{3 + 2 j}{- 7 + 4 j}$

Step 1

Reorder $3$ and $2 j$ .

$\frac{2 j + 3}{- 7 + 4 j}$

Step 2

Reorder $- 7$ and $4 j$ .

$\frac{2 j + 3}{4 j - 7}$

Step 3

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$4 j$

$7$

$2 j$

$3$

Step 4

Divide the highest order term in the dividend $2 j$ by the highest order term in divisor $4 j$ .

					$\frac{1}{2}$
	$4 j$	-	$7$		$2 j$	+	$3$

Step 5

Multiply the new quotient term by the divisor.

Step 6

The expression needs to be subtracted from the dividend, so change all the signs in $2 j - \frac{7}{2}$

Step 7

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

Step 8

The final answer is the quotient plus the remainder over the divisor.

$\frac{1}{2} + \frac{13}{2 (4 j - 7)}$