Basic Math Examples

$\frac{b^{2}}{b - 2} - \frac{8 b - 12}{b - 2}$

Step 1

Simplify terms.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{b^{2} - (8 b - 12)}{b - 2}$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$\frac{b^{2} - (8 b) - - 12}{b - 2}$

Step 1.2.2

Multiply $8$ by $- 1$ .

$\frac{b^{2} - 8 b - - 12}{b - 2}$

Step 1.2.3

Multiply $- 1$ by $- 12$ .

$\frac{b^{2} - 8 b + 12}{b - 2}$

Step 2

Factor $b^{2} - 8 b + 12$ 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 $12$ and whose sum is $- 8$ .

$- 6, - 2$

Step 2.2

Write the factored form using these integers.

$\frac{(b - 6) (b - 2)}{b - 2}$

Step 3

Cancel the common factor of $b - 2$ .

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Step 3.1

Cancel the common factor.

$\frac{(b - 6) (b - 2)}{b - 2}$

Step 3.2

Divide $b - 6$ by $1$ .

$b - 6$