Precalculus Examples

$\frac{5 x - 7}{4 - x}$

Step 1

Reorder $4$ and $- x$ .

$\frac{5 x - 7}{- x + 4}$

Step 2

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

$x$

$4$

$5 x$

$7$

Step 3

Divide the highest order term in the dividend $5 x$ by the highest order term in divisor $- x$ .

				-	$5$
-	$x$	+	$4$		$5 x$	-	$7$

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 $5 x - 20$

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.

$- 5 + \frac{13}{- x + 4}$