Divide ((a^2-2a+1)/6)÷(a^2-1)

$\frac{a^{2} - 2 a + 1}{6} \div (a^{2} - 1)$

Step 1

Expand $\frac{a^{2} - 2 a + 1}{6}$ .

Split the fraction $\frac{a^{2} - 2 a + 1}{6}$ into two fractions.

$\frac{\frac{a^{2} - 2 a}{6} + \frac{1}{6}}{a^{2} - 1}$

Split the fraction $\frac{a^{2} - 2 a}{6}$ into two fractions.

$\frac{\frac{a^{2}}{6} + \frac{- 2 a}{6} + \frac{1}{6}}{a^{2} - 1}$

Step 2

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

$a^{2}$

$0 a$

$1$

$\frac{a^{2}}{6}$

$\frac{- 2 a}{6}$

$\frac{1}{6}$

Step 3

Divide the highest order term in the dividend $\frac{a^{2}}{6}$ by the highest order term in divisor $a^{2}$ .

							$\frac{1}{6}$
	$a^{2}$	+	$0 a$	-	$1$		$\frac{a^{2}}{6}$	+	$\frac{- 2 a}{6}$	+	$\frac{1}{6}$

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 $\frac{a^{2}}{6} + 0 - \frac{1}{6}$

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.

$\frac{1}{6} + \frac{- \frac{a}{3} + \frac{1}{3}}{a^{2} - 1}$