Precalculus Examples

$\frac{4 x + 3}{2 x - 5}$

Step 1

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

$2 x$

$5$

$4 x$

$3$

Step 2

Divide the highest order term in the dividend $4 x$ by the highest order term in divisor $2 x$ .

					$2$
	$2 x$	-	$5$		$4 x$	+	$3$

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 $4 x - 10$

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.

$2 + \frac{13}{2 x - 5}$