Finite Math Examples

$\frac{8 x^{2} y^{2} + 6 x y^{2} - 8 y^{2}}{2 x^{2} y}$

Step 1

Divide each term in the denominator by $2$ to make the coefficient of linear factor variable $1$ .

$\frac{1}{2} \cdot \frac{- 8 y^{2} + 8 x^{2} y^{2} + 6 y^{2} x}{x^{2} y}$

Step 2

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

$0$	$- 8$	$8$	$6$

Step 3

The first number in the dividend $(- 8)$ is put into the first position of the result area (below the horizontal line).

$0$	$- 8$	$8$	$6$

	$- 8$

Step 4

Multiply the newest entry in the result $(- 8)$ by the divisor $(0)$ and place the result of $(0)$ under the next term in the dividend $(8)$ .

$0$	$- 8$	$8$	$6$
		$0$
	$- 8$

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.

$0$	$- 8$	$8$	$6$
		$0$
	$- 8$	$8$

Step 6

Multiply the newest entry in the result $(8)$ by the divisor $(0)$ and place the result of $(0)$ under the next term in the dividend $(6)$ .

$0$	$- 8$	$8$	$6$
		$0$	$0$
	$- 8$	$8$

Step 7

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

$0$	$- 8$	$8$	$6$
		$0$	$0$
	$- 8$	$8$	$6$

Step 8

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

$(\frac{1}{2}) \cdot ((- 8) y + 8 + \frac{6}{x^{2} y})$

Step 9

Simplify the quotient polynomial.

$(\frac{1}{2}) \cdot (- 8 y + 8 + \frac{6}{x^{2} y})$

Step 10

Simplify.

Tap for more steps...

Step 10.1

Distribute.

Tap for more steps...

Step 10.1.1

Apply the distributive property.

$\frac{1}{2} \cdot (- 8 y + 8) + \frac{1}{2} \cdot \frac{6}{x^{2} y}$

Step 10.1.2

Apply the distributive property.

$\frac{1}{2} \cdot (- 8 y) + \frac{1}{2} \cdot 8 + \frac{1}{2} \cdot \frac{6}{x^{2} y}$

Step 10.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 10.2.1

Factor $2$ out of $- 8 y$ .

$\frac{1}{2} \cdot (2 (- 4 y)) + \frac{1}{2} \cdot 8 + \frac{1}{2} \cdot \frac{6}{x^{2} y}$

Step 10.2.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 (- 4 y)) + \frac{1}{2} \cdot 8 + \frac{1}{2} \cdot \frac{6}{x^{2} y}$

Step 10.2.3

Rewrite the expression.

$- 4 y + \frac{1}{2} \cdot 8 + \frac{1}{2} \cdot \frac{6}{x^{2} y}$

Step 10.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 10.3.1

Factor $2$ out of $8$ .

$- 4 y + \frac{1}{2} \cdot (2 (4)) + \frac{1}{2} \cdot \frac{6}{x^{2} y}$

Step 10.3.2

Cancel the common factor.

$- 4 y + \frac{1}{2} \cdot (2 \cdot 4) + \frac{1}{2} \cdot \frac{6}{x^{2} y}$

Step 10.3.3

Rewrite the expression.

$- 4 y + 4 + \frac{1}{2} \cdot \frac{6}{x^{2} y}$

Step 10.4

Combine.

$- 4 y + 4 + \frac{1 \cdot 6}{2 (x^{2} y)}$

Step 10.5

Cancel the common factor of $6$ and $2$ .

Tap for more steps...

Step 10.5.1

Factor $2$ out of $1 \cdot 6$ .

$- 4 y + 4 + \frac{2 (1 \cdot 3)}{2 (x^{2} y)}$

Step 10.5.2

Cancel the common factors.

Tap for more steps...

Step 10.5.2.1

Cancel the common factor.

$- 4 y + 4 + \frac{2 (1 \cdot 3)}{2 (x^{2} y)}$

Step 10.5.2.2

Rewrite the expression.

$- 4 y + 4 + \frac{1 \cdot 3}{x^{2} y}$

Step 10.6

Multiply $3$ by $1$ .

$- 4 y + 4 + \frac{3}{x^{2} y}$