Precalculus Examples

$\frac{0.474 x + x^{2}}{9.81 a - 2 - x}$

Step 1

Reorder $0.474 x$ and $x^{2}$ .

$\frac{x^{2} + 0.474 x}{9.81 a - 2 - x}$

Step 2

Move $- 2$ .

$\frac{x^{2} + 0.474 x}{9.81 a - x - 2}$

Step 3

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

$x$

$9.81 a$

$2$

$x^{2}$

$0.474 x$

$0$

Step 4

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

						-	$x$
-	$x$	+	$9.81 a$	-	$2$		$x^{2}$	+	$0.474 x$	+	$0$

Step 5

Multiply the new quotient term by the divisor.

						-	$x$
-	$x$	+	$9.81 a$	-	$2$		$x^{2}$	+	$0.474 x$	+	$0$
						+	$x^{2}$	-	$9.81 x a$	+	$2 x$

Step 6

The expression needs to be subtracted from the dividend, so change all the signs in $x^{2} - 9.81 x a + 2 x$

						-	$x$
-	$x$	+	$9.81 a$	-	$2$		$x^{2}$	+	$0.474 x$	+	$0$
						-	$x^{2}$	+	$9.81 x a$	-	$2 x$

Step 7

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

						-	$x$
-	$x$	+	$9.81 a$	-	$2$		$x^{2}$	+	$0.474 x$	+	$0$
						-	$x^{2}$	+	$9.81 x a$	-	$2 x$
								+	$0.474 x$	-	$2 x$

Step 8

Divide the highest order term in the dividend $0.474 x$ by the highest order term in divisor $- x$ .

						-	$x$	-	$0.474$
-	$x$	+	$9.81 a$	-	$2$		$x^{2}$	+	$0.474 x$	+	$0$
						-	$x^{2}$	+	$9.81 x a$	-	$2 x$
								+	$0.474 x$	-	$2 x$

Step 9

Multiply the new quotient term by the divisor.

$x$

$0.474$

$x$

$9.81 a$

$2$

$x^{2}$

$0.474 x$

$0$

$x^{2}$

$9.81 x a$

$2 x$

$0.474 x$

$2 x$

$0.474 x$

$4.64994 a$

$0.948$

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $0.474 x - 4.64994 a + 0.948$

						-	$x$	-	$0.474$
-	$x$	+	$9.81 a$	-	$2$		$x^{2}$	+	$0.474 x$	+	$0$
						-	$x^{2}$	+	$9.81 x a$	-	$2 x$
								+	$0.474 x$	-	$2 x$
								-	$0.474 x$	+	$4.64994 a$	-	$0.948$

Step 11

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

						-	$x$	-	$0.474$
-	$x$	+	$9.81 a$	-	$2$		$x^{2}$	+	$0.474 x$	+	$0$
						-	$x^{2}$	+	$9.81 x a$	-	$2 x$
								+	$0.474 x$	-	$2 x$
								-	$0.474 x$	+	$4.64994 a$	-	$0.948$
										-	$2 x$	-	$0.948$

Step 12

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

						-	$x$	-	$0.474$	+	$2$
-	$x$	+	$9.81 a$	-	$2$		$x^{2}$	+	$0.474 x$	+	$0$
						-	$x^{2}$	+	$9.81 x a$	-	$2 x$
								+	$0.474 x$	-	$2 x$
								-	$0.474 x$	+	$4.64994 a$	-	$0.948$
										-	$2 x$	-	$0.948$

Step 13

Multiply the new quotient term by the divisor.

						-	$x$	-	$0.474$	+	$2$
-	$x$	+	$9.81 a$	-	$2$		$x^{2}$	+	$0.474 x$	+	$0$
						-	$x^{2}$	+	$9.81 x a$	-	$2 x$
								+	$0.474 x$	-	$2 x$
								-	$0.474 x$	+	$4.64994 a$	-	$0.948$
										-	$2 x$	-	$0.948$
										-	$2 x$	+	$19.62 a$	-	$4$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $- 2 x + 19.62 a - 4$

						-	$x$	-	$0.474$	+	$2$
-	$x$	+	$9.81 a$	-	$2$		$x^{2}$	+	$0.474 x$	+	$0$
						-	$x^{2}$	+	$9.81 x a$	-	$2 x$
								+	$0.474 x$	-	$2 x$
								-	$0.474 x$	+	$4.64994 a$	-	$0.948$
										-	$2 x$	-	$0.948$
										+	$2 x$	-	$19.62 a$	+	$4$

Step 15

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

						-	$x$	-	$0.474$	+	$2$
-	$x$	+	$9.81 a$	-	$2$		$x^{2}$	+	$0.474 x$	+	$0$
						-	$x^{2}$	+	$9.81 x a$	-	$2 x$
								+	$0.474 x$	-	$2 x$
								-	$0.474 x$	+	$4.64994 a$	-	$0.948$
										-	$2 x$	-	$0.948$
										+	$2 x$	-	$19.62 a$	+	$4$
												-	$0.948$	+	$4$

Step 16

The final answer is the quotient plus the remainder over the divisor.

$- x + 1.526 + \frac{3.052}{- x + 9.81 a - 2}$