Precalculus Examples

$\frac{7 x - 2}{2 x - 1}$

Step 1

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

$2 x$

$1$

$7 x$

$2$

Step 2

Divide the highest order term in the dividend $7 x$ by the highest order term in divisor $2 x$ .

					$\frac{7}{2}$
	$2 x$	-	$1$		$7 x$	-	$2$

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 $7 x - \frac{7}{2}$

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.

$\frac{7}{2} + \frac{3}{2 (2 x - 1)}$

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