Precalculus Examples

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

Step 1

Reorder $2$ and $- x$ .

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

Step 2

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

$x$

$2$

$2 x$

$5$

Step 3

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

				-	$2$
-	$x$	+	$2$		$2 x$	-	$5$

Step 4

Multiply the new quotient term by the divisor.

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $2 x - 4$

Step 6

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

Step 7

The final answer is the quotient plus the remainder over the divisor.

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