Algebra Examples

$\frac{a - 3}{7} \div \frac{3 - a}{21}$

Step 1

Split the fraction $\frac{a - 3}{7}$ into two fractions.

$\frac{\frac{a}{7} + \frac{- 3}{7}}{\frac{3 - a}{21}}$

Step 2

Expand $\frac{3 - a}{21}$ .

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Step 2.1

Split the fraction $\frac{3 - a}{21}$ into two fractions.

$\frac{\frac{a}{7} + \frac{- 3}{7}}{\frac{3}{21} + \frac{- a}{21}}$

Step 2.2

Reorder $\frac{3}{21}$ and $\frac{- a}{21}$ .

$\frac{\frac{a}{7} + \frac{- 3}{7}}{\frac{- a}{21} + \frac{3}{21}}$

Step 3

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

$\frac{- a}{21}$

$\frac{3}{21}$

$\frac{a}{7}$

$\frac{- 3}{7}$

Step 4

Divide the highest order term in the dividend $\frac{a}{7}$ by the highest order term in divisor $\frac{- a}{21}$ .

				-	$3$
	$\frac{- a}{21}$	+	$\frac{3}{21}$		$\frac{a}{7}$	+	$\frac{- 3}{7}$

Step 5

Multiply the new quotient term by the divisor.

Step 6

The expression needs to be subtracted from the dividend, so change all the signs in $\frac{a}{7} - \frac{3}{7}$

Step 7

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

Step 8

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

$- 3$