Basic Math Examples

$\frac{4 s}{s^{2} - 6 s + 9} - \frac{12}{s^{2} - 6 s + 9}$

Step 1

Simplify terms.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{4 s - 12}{s^{2} - 6 s + 9}$

Step 1.2

Factor $4$ out of $4 s - 12$ .

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Step 1.2.1

Factor $4$ out of $4 s$ .

$\frac{4 (s) - 12}{s^{2} - 6 s + 9}$

Step 1.2.2

Factor $4$ out of $- 12$ .

$\frac{4 s + 4 \cdot - 3}{s^{2} - 6 s + 9}$

Step 1.2.3

Factor $4$ out of $4 s + 4 \cdot - 3$ .

$\frac{4 (s - 3)}{s^{2} - 6 s + 9}$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $9$ as $3^{2}$ .

$\frac{4 (s - 3)}{s^{2} - 6 s + 3^{2}}$

Step 2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$6 s = 2 \cdot s \cdot 3$

Step 2.3

Rewrite the polynomial.

$\frac{4 (s - 3)}{s^{2} - 2 \cdot s \cdot 3 + 3^{2}}$

Step 2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = s$ and $b = 3$ .

$\frac{4 (s - 3)}{{(s - 3)}^{2}}$

Step 3

Cancel the common factor of $s - 3$ and ${(s - 3)}^{2}$ .

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Step 3.1

Factor $s - 3$ out of $4 (s - 3)$ .

$\frac{(s - 3) \cdot 4}{{(s - 3)}^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $s - 3$ out of ${(s - 3)}^{2}$ .

$\frac{(s - 3) \cdot 4}{(s - 3) (s - 3)}$

Step 3.2.2

Cancel the common factor.

$\frac{(s - 3) \cdot 4}{(s - 3) (s - 3)}$

Step 3.2.3

Rewrite the expression.

$\frac{4}{s - 3}$