Calculus Examples

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

Step 1

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

$x$

$3$

$3 x$

$2$

Step 2

Divide the highest order term in the dividend $3 x$ by the highest order term in divisor $x$ .

					$3$
	$x$	-	$3$		$3 x$	-	$2$

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 $3 x - 9$

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.

$3 + \frac{7}{x - 3}$

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