Finite Math Examples

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

Step 1

Divide each term in the denominator by $2$ to make the coefficient of linear factor variable $1$ .

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

Step 2

Place the numbers representing the divisor and the dividend into a division-like configuration.

$\frac{1}{2}$	$2$	$1$	$1$

Step 3

The first number in the dividend $(2)$ is put into the first position of the result area (below the horizontal line).

$\frac{1}{2}$	$2$	$1$	$1$

	$2$

Step 4

Multiply the newest entry in the result $(2)$ by the divisor $(\frac{1}{2})$ and place the result of $(1)$ under the next term in the dividend $(1)$ .

$\frac{1}{2}$	$2$	$1$	$1$
		$1$
	$2$

Step 5

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$\frac{1}{2}$	$2$	$1$	$1$
		$1$
	$2$	$2$

Step 6

Multiply the newest entry in the result $(2)$ by the divisor $(\frac{1}{2})$ and place the result of $(1)$ under the next term in the dividend $(1)$ .

$\frac{1}{2}$	$2$	$1$	$1$
		$1$	$1$
	$2$	$2$

Step 7

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$\frac{1}{2}$	$2$	$1$	$1$
		$1$	$1$
	$2$	$2$	$2$

Step 8

All numbers except the last become the coefficients of the quotient polynomial. The last value in the result line is the remainder.

$(\frac{1}{2}) \cdot ((2) x + 2 + \frac{2}{\frac{2 x - 1}{2}})$

Step 9

Simplify the quotient polynomial.

$(\frac{1}{2}) \cdot (2 x + 2 + \frac{4}{2 x - 1})$

Step 10

Simplify.

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Step 10.1

Distribute.

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Step 10.1.1

Apply the distributive property.

$\frac{1}{2} \cdot (2 x + 2) + \frac{1}{2} \cdot \frac{4}{2 x - 1}$

Step 10.1.2

Apply the distributive property.

$\frac{1}{2} \cdot (2 x) + \frac{1}{2} \cdot 2 + \frac{1}{2} \cdot \frac{4}{2 x - 1}$

Step 10.2

Cancel the common factor of $2$ .

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Step 10.2.1

Factor $2$ out of $2 x$ .

$\frac{1}{2} \cdot (2 (x)) + \frac{1}{2} \cdot 2 + \frac{1}{2} \cdot \frac{4}{2 x - 1}$

Step 10.2.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 x) + \frac{1}{2} \cdot 2 + \frac{1}{2} \cdot \frac{4}{2 x - 1}$

Step 10.2.3

Rewrite the expression.

$x + \frac{1}{2} \cdot 2 + \frac{1}{2} \cdot \frac{4}{2 x - 1}$

Step 10.3

Cancel the common factor of $2$ .

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Step 10.3.1

Cancel the common factor.

$x + \frac{1}{2} \cdot 2 + \frac{1}{2} \cdot \frac{4}{2 x - 1}$

Step 10.3.2

Rewrite the expression.

$x + 1 + \frac{1}{2} \cdot \frac{4}{2 x - 1}$

Step 10.4

Cancel the common factor of $2$ .

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Step 10.4.1

Factor $2$ out of $4$ .

$x + 1 + \frac{1}{2} \cdot \frac{2 (2)}{2 x - 1}$

Step 10.4.2

Cancel the common factor.

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

Step 10.4.3

Rewrite the expression.

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