Pre-Algebra Examples

$- \frac{3 x - 1}{x + 3}$

Step 1

Expand $- (3 x - 1)$ .

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Step 1.1

Negate $3 x - 1$ .

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Remove parentheses.

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

Step 1.4

Multiply $- 1$ by $3$ .

$\frac{- 3 x + 1}{x + 3}$

Step 1.5

Multiply $- 1$ by $- 1$ .

$\frac{- 3 x + 1}{x + 3}$

Step 2

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

$x$

$3$

$3 x$

$1$

Step 3

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

				-	$3$
	$x$	+	$3$	-	$3 x$	+	$1$

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 $- 3 x - 9$

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.

$- 3 + \frac{10}{x + 3}$