Precalculus Examples

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

Step 1

Divide each term in the denominator by $4$ to make the coefficient of linear factor variable $1$ .

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

Step 2

Place the numbers representing the divisor and the dividend into a division-like configuration.

$\frac{7}{4}$	$2$	$3$

Step 3

The first number in the dividend $(2)$ is put into the first position of the result area (below the horizontal line).

$\frac{7}{4}$	$2$	$3$

	$2$

Step 4

Multiply the newest entry in the result $(2)$ by the divisor $(\frac{7}{4})$ and place the result of $(\frac{7}{2})$ under the next term in the dividend $(3)$ .

$\frac{7}{4}$	$2$	$3$
		$\frac{7}{2}$
	$2$

Step 5

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$\frac{7}{4}$	$2$	$3$
		$\frac{7}{2}$
	$2$	$\frac{13}{2}$

Step 6

All numbers except the last become the coefficients of the quotient polynomial. The last value in the result line is the remainder.

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

Step 7

Simplify the quotient polynomial.

$(\frac{1}{4}) \cdot (2 + \frac{26}{4 j - 7})$

Step 8

Simplify.

Tap for more steps...

Step 8.1

Apply the distributive property.

$\frac{1}{4} \cdot 2 + \frac{1}{4} \cdot \frac{26}{4 j - 7}$

Step 8.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 8.2.1

Factor $2$ out of $4$ .

$\frac{1}{2 (2)} \cdot 2 + \frac{1}{4} \cdot \frac{26}{4 j - 7}$

Step 8.2.2

Cancel the common factor.

$\frac{1}{2 \cdot 2} \cdot 2 + \frac{1}{4} \cdot \frac{26}{4 j - 7}$

Step 8.2.3

Rewrite the expression.

$\frac{1}{2} + \frac{1}{4} \cdot \frac{26}{4 j - 7}$

Step 8.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 8.3.1

Factor $2$ out of $4$ .

$\frac{1}{2} + \frac{1}{2 (2)} \cdot \frac{26}{4 j - 7}$

Step 8.3.2

Factor $2$ out of $26$ .

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

Step 8.3.3

Cancel the common factor.

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

Step 8.3.4

Rewrite the expression.

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

Step 8.4

Multiply $\frac{1}{2}$ by $\frac{13}{4 j - 7}$ .

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