Pre-Algebra Examples

$\frac{b^{2} + 5 b - 36}{\frac{b}{2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(b^{2} + 5 b - 36) \frac{2}{b}$

Step 2

Multiply $b^{2} + 5 b - 36$ by $\frac{2}{b}$ .

$\frac{(b^{2} + 5 b - 36) \cdot 2}{b}$

Step 3

Factor $b^{2} + 5 b - 36$ using the AC method.

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Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 36$ and whose sum is $5$ .

$- 4, 9$

Step 3.2

Write the factored form using these integers.

$\frac{(b - 4) (b + 9) \cdot 2}{b}$

Step 4

Move $2$ to the left of $(b - 4) (b + 9)$ .

$\frac{2 (b - 4) (b + 9)}{b}$

Step 5

Apply the distributive property.

$\frac{(2 b + 2 \cdot - 4) (b + 9)}{b}$

Step 6

Multiply $2$ by $- 4$ .

$\frac{(2 b - 8) (b + 9)}{b}$

Step 7

Expand $(2 b - 8) (b + 9)$ using the FOIL Method.

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Step 7.1

Apply the distributive property.

$\frac{2 b (b + 9) - 8 (b + 9)}{b}$

Step 7.2

Apply the distributive property.

$\frac{2 b \cdot b + 2 b \cdot 9 - 8 (b + 9)}{b}$

Step 7.3

Apply the distributive property.

$\frac{2 b \cdot b + 2 b \cdot 9 - 8 b - 8 \cdot 9}{b}$

Step 8

Simplify and combine like terms.

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Step 8.1

Simplify each term.

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Step 8.1.1

Multiply $b$ by $b$ by adding the exponents.

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Step 8.1.1.1

Move $b$ .

$\frac{2 (b \cdot b) + 2 b \cdot 9 - 8 b - 8 \cdot 9}{b}$

Step 8.1.1.2

Multiply $b$ by $b$ .

$\frac{2 b^{2} + 2 b \cdot 9 - 8 b - 8 \cdot 9}{b}$

Step 8.1.2

Multiply $9$ by $2$ .

$\frac{2 b^{2} + 18 b - 8 b - 8 \cdot 9}{b}$

Step 8.1.3

Multiply $- 8$ by $9$ .

$\frac{2 b^{2} + 18 b - 8 b - 72}{b}$

Step 8.2

Subtract $8 b$ from $18 b$ .

$\frac{2 b^{2} + 10 b - 72}{b}$

Step 9

Split the fraction $\frac{2 b^{2} + 10 b - 72}{b}$ into two fractions.

$\frac{2 b^{2} + 10 b}{b} + \frac{- 72}{b}$

Step 10

Split the fraction $\frac{2 b^{2} + 10 b}{b}$ into two fractions.

$\frac{2 b^{2}}{b} + \frac{10 b}{b} + \frac{- 72}{b}$

Step 11

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

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Step 11.1

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

$\frac{b (2 b)}{b} + \frac{10 b}{b} + \frac{- 72}{b}$

Step 11.2

Cancel the common factors.

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Step 11.2.1

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

$\frac{b (2 b)}{b^{1}} + \frac{10 b}{b} + \frac{- 72}{b}$

Step 11.2.2

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

$\frac{b (2 b)}{b \cdot 1} + \frac{10 b}{b} + \frac{- 72}{b}$

Step 11.2.3

Cancel the common factor.

$\frac{b (2 b)}{b \cdot 1} + \frac{10 b}{b} + \frac{- 72}{b}$

Step 11.2.4

Rewrite the expression.

$\frac{2 b}{1} + \frac{10 b}{b} + \frac{- 72}{b}$

Step 11.2.5

Divide $2 b$ by $1$ .

$2 b + \frac{10 b}{b} + \frac{- 72}{b}$

Step 12

Cancel the common factor of $b$ .

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Step 12.1

Cancel the common factor.

$2 b + \frac{10 b}{b} + \frac{- 72}{b}$

Step 12.2

Divide $10$ by $1$ .

$2 b + 10 + \frac{- 72}{b}$

Step 13

Move the negative in front of the fraction.

$2 b + 10 - \frac{72}{b}$