Basic Math Examples

$\frac{b^{2} - 9 b + 20}{b^{2} - 10 b + 24} \div \frac{b^{2} + 4 b}{b^{2} - 2 b - 24}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{b^{2} - 9 b + 20}{b^{2} - 10 b + 24} \cdot \frac{b^{2} - 2 b - 24}{b^{2} + 4 b}$

Step 2

Factor $b^{2} - 9 b + 20$ using the AC method.

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Step 2.1

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 $20$ and whose sum is $- 9$ .

$- 5, - 4$

Step 2.2

Write the factored form using these integers.

$\frac{(b - 5) (b - 4)}{b^{2} - 10 b + 24} \cdot \frac{b^{2} - 2 b - 24}{b^{2} + 4 b}$

Step 3

Factor $b^{2} - 10 b + 24$ 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 $24$ and whose sum is $- 10$ .

$- 6, - 4$

Step 3.2

Write the factored form using these integers.

$\frac{(b - 5) (b - 4)}{(b - 6) (b - 4)} \cdot \frac{b^{2} - 2 b - 24}{b^{2} + 4 b}$

Step 4

Cancel the common factor of $b - 4$ .

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Step 4.1

Cancel the common factor.

$\frac{(b - 5) (b - 4)}{(b - 6) (b - 4)} \cdot \frac{b^{2} - 2 b - 24}{b^{2} + 4 b}$

Step 4.2

Rewrite the expression.

$\frac{b - 5}{b - 6} \cdot \frac{b^{2} - 2 b - 24}{b^{2} + 4 b}$

Step 5

Factor $b^{2} - 2 b - 24$ using the AC method.

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Step 5.1

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 $- 24$ and whose sum is $- 2$ .

$- 6, 4$

Step 5.2

Write the factored form using these integers.

$\frac{b - 5}{b - 6} \cdot \frac{(b - 6) (b + 4)}{b^{2} + 4 b}$

Step 6

Simplify terms.

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Step 6.1

Factor $b$ out of $b^{2} + 4 b$ .

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Step 6.1.1

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

$\frac{b - 5}{b - 6} \cdot \frac{(b - 6) (b + 4)}{b \cdot b + 4 b}$

Step 6.1.2

Factor $b$ out of $4 b$ .

$\frac{b - 5}{b - 6} \cdot \frac{(b - 6) (b + 4)}{b \cdot b + b \cdot 4}$

Step 6.1.3

Factor $b$ out of $b \cdot b + b \cdot 4$ .

$\frac{b - 5}{b - 6} \cdot \frac{(b - 6) (b + 4)}{b (b + 4)}$

Step 6.2

Cancel the common factor of $b - 6$ .

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Step 6.2.1

Cancel the common factor.

$\frac{b - 5}{b - 6} \cdot \frac{(b - 6) (b + 4)}{b (b + 4)}$

Step 6.2.2

Rewrite the expression.

$(b - 5) \frac{b + 4}{b (b + 4)}$

Step 6.3

Cancel the common factor of $b + 4$ .

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Step 6.3.1

Cancel the common factor.

$(b - 5) \frac{b + 4}{b (b + 4)}$

Step 6.3.2

Rewrite the expression.

$(b - 5) \frac{1}{b}$

Step 6.4

Multiply $b - 5$ by $\frac{1}{b}$ .

$\frac{b - 5}{b}$