Algebra Examples

$\frac{2 b^{2} + b - 8}{2 b}$

Step 1

Split the fraction $\frac{2 b^{2} + b - 8}{2 b}$ into two fractions.

$\frac{2 b^{2} + b}{2 b} + \frac{- 8}{2 b}$

Step 2

Split the fraction $\frac{2 b^{2} + b}{2 b}$ into two fractions.

$\frac{2 b^{2}}{2 b} + \frac{b}{2 b} + \frac{- 8}{2 b}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

$\frac{2 b^{2}}{2 b} + \frac{b}{2 b} + \frac{- 8}{2 b}$

Step 3.2

Rewrite the expression.

$\frac{b^{2}}{b} + \frac{b}{2 b} + \frac{- 8}{2 b}$

Step 4

Cancel the common factor of $b^{2}$ and $b$ .

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Step 4.1

Factor $b$ out of $b^{2}$ .

$\frac{b \cdot b}{b} + \frac{b}{2 b} + \frac{- 8}{2 b}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Raise $b$ to the power of $1$ .

$\frac{b \cdot b}{b^{1}} + \frac{b}{2 b} + \frac{- 8}{2 b}$

Step 4.2.2

Factor $b$ out of $b^{1}$ .

$\frac{b \cdot b}{b \cdot 1} + \frac{b}{2 b} + \frac{- 8}{2 b}$

Step 4.2.3

Cancel the common factor.

$\frac{b \cdot b}{b \cdot 1} + \frac{b}{2 b} + \frac{- 8}{2 b}$

Step 4.2.4

Rewrite the expression.

$\frac{b}{1} + \frac{b}{2 b} + \frac{- 8}{2 b}$

Step 4.2.5

Divide $b$ by $1$ .

$b + \frac{b}{2 b} + \frac{- 8}{2 b}$

Step 5

Cancel the common factor of $b$ .

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Step 5.1

Cancel the common factor.

$b + \frac{b}{2 b} + \frac{- 8}{2 b}$

Step 5.2

Rewrite the expression.

$b + \frac{1}{2} + \frac{- 8}{2 b}$

Step 6

Cancel the common factor of $- 8$ and $2$ .

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Step 6.1

Factor $2$ out of $- 8$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $2 b$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

$b + \frac{1}{2} + \frac{- 4}{b}$

Step 7

Move the negative in front of the fraction.

$b + \frac{1}{2} - \frac{4}{b}$