Divide Using Long Polynomial Division (36x5/6)÷(4x2/3)

$(36 x \frac{5}{6}) \div (4 x \frac{2}{3})$

Step 1

Combine $36 x$ and $\frac{5}{6}$ .

$\frac{\frac{36 x \cdot 5}{6}}{4 x (\frac{2}{3})}$

Step 2

Combine $4 x$ and $\frac{2}{3}$ .

$\frac{\frac{36 x \cdot 5}{6}}{\frac{4 x \cdot 2}{3}}$

Step 3

Turn the denominator into a polynomial.

Start expanding.

$4 x (\frac{2}{3})$

Combine $4 x$ and $\frac{2}{3}$ .

$\frac{4 x \cdot 2}{3}$

Multiply $2$ by $4$ .

$\frac{8 x}{3}$

Step 4

Turn the numerator into a polynomial.

Start expanding.

$36 x (\frac{5}{6})$

Combine $36 x$ and $\frac{5}{6}$ .

$\frac{36 x \cdot 5}{6}$

Multiply $5$ by $36$ .

$\frac{180 x}{6}$

Step 5

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

$\frac{8 x}{3}$

$0$

$\frac{180 x}{6}$

$0$

Step 6

Divide the highest order term in the dividend $\frac{180 x}{6}$ by the highest order term in divisor $\frac{8 x}{3}$ .

					$\frac{45}{4}$
	$\frac{8 x}{3}$	+	$0$		$\frac{180 x}{6}$	+	$0$

Step 7

Multiply the new quotient term by the divisor.

Step 8

The expression needs to be subtracted from the dividend, so change all the signs in $30 x + 0$

Step 9

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

Step 10

Since the remander is $0$ , the final answer is the quotient.

$\frac{45}{4}$