Basic Math Examples

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

Step 1

Factor by grouping.

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Step 1.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 4 \cdot - 9 = - 36$ and whose sum is $b = 9$ .

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Step 1.1.1

Factor $9$ out of $9 s$ .

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

Step 1.1.2

Rewrite $9$ as $- 3$ plus $12$

$\frac{4 s^{2} + (- 3 + 12) s - 9}{s t} \cdot \frac{6 s}{s + 3}$

Step 1.1.3

Apply the distributive property.

$\frac{4 s^{2} - 3 s + 12 s - 9}{s t} \cdot \frac{6 s}{s + 3}$

Step 1.2

Factor out the greatest common factor from each group.

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Step 1.2.1

Group the first two terms and the last two terms.

$\frac{(4 s^{2} - 3 s) + 12 s - 9}{s t} \cdot \frac{6 s}{s + 3}$

Step 1.2.2

Factor out the greatest common factor (GCF) from each group.

$\frac{s (4 s - 3) + 3 (4 s - 3)}{s t} \cdot \frac{6 s}{s + 3}$

Step 1.3

Factor the polynomial by factoring out the greatest common factor, $4 s - 3$ .

$\frac{(4 s - 3) (s + 3)}{s t} \cdot \frac{6 s}{s + 3}$

Step 2

Cancel the common factor of $s + 3$ .

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Step 2.1

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

$\frac{(s + 3) (4 s - 3)}{s t} \cdot \frac{6 s}{s + 3}$

Step 2.2

Cancel the common factor.

$\frac{(s + 3) (4 s - 3)}{s t} \cdot \frac{6 s}{s + 3}$

Step 2.3

Rewrite the expression.

$\frac{4 s - 3}{s t} \cdot (6 s)$

Step 3

Cancel the common factor of $s$ .

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Step 3.1

Factor $s$ out of $s t$ .

$\frac{4 s - 3}{s (t)} \cdot (6 s)$

Step 3.2

Factor $s$ out of $6 s$ .

$\frac{4 s - 3}{s (t)} \cdot (s \cdot 6)$

Step 3.3

Cancel the common factor.

$\frac{4 s - 3}{s t} \cdot (s \cdot 6)$

Step 3.4

Rewrite the expression.

$\frac{4 s - 3}{t} \cdot 6$

Step 4

Combine $\frac{4 s - 3}{t}$ and $6$ .

$\frac{(4 s - 3) \cdot 6}{t}$

Step 5

Move $6$ to the left of $4 s - 3$ .

$\frac{6 (4 s - 3)}{t}$