Algebra Examples

$(x \cdot 3 + y \cdot 3) \div (x - y)$

Step 1

Expand $x \cdot 3 + y \cdot 3$ .

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Step 1.1

Reorder $x$ and $3$ .

$\frac{3 \cdot x + y \cdot 3}{x - y}$

Step 1.2

Reorder $y$ and $3$ .

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

Step 2

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

$x$

$y$

$3 x$

$3 y$

Step 3

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

					$3$
	$x$	-	$y$		$3 x$	+	$3 y$

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 $3 x - 3 y$

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.

$3 + \frac{6 y}{x - y}$