Pre-Algebra Examples

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

Step 1

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

$x^{2}$

$2 x$

$3$

$x^{2}$

$x$

$2$

Step 2

Divide the highest order term in the dividend $x^{2}$ by the highest order term in divisor $x^{2}$ .

							$1$
	$x^{2}$	-	$2 x$	-	$3$		$x^{2}$	-	$x$	-	$2$

Step 3

Multiply the new quotient term by the divisor.

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $x^{2} - 2 x - 3$

Step 5

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

Step 6

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

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