Calculus Examples

$\frac{x^{2}}{1 - x^{2}}$

Step 1

Reorder $1$ and $- x^{2}$ .

$\frac{x^{2}}{- x^{2} + 1}$

Step 2

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

$x^{2}$

$0 x$

$1$

$x^{2}$

$0 x$

$0$

Step 3

Divide the highest order term in the dividend $x^{2}$ by the highest order term in divisor $- x^{2}$ .

						-	$1$
-	$x^{2}$	+	$0 x$	+	$1$		$x^{2}$	+	$0 x$	+	$0$

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 $x^{2} + 0 - 1$

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.

$- 1 + \frac{1}{- x^{2} + 1}$