Calculus Examples

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

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

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

$0$ .

x

$x$

3

$3$

3 x

$3 x$

2

$2$

Step 2

Divide the highest order term in the dividend

3 x

$3 x$ by the highest order term in divisor

x

$x$ .

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

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

$3 x - 9$

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}

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

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