Precalculus Examples

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

Step 1

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

$3 x$

$2$

$4 x$

$7$

Step 2

Divide the highest order term in the dividend $4 x$ by the highest order term in divisor $3 x$ .

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

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 $4 x - \frac{8}{3}$

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.

$\frac{4}{3} + \frac{29}{3 (3 x - 2)}$