Basic Math Examples

$\frac{8 w - 2 w^{2} - 6}{w - 1}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $2$ out of $8 w - 2 w^{2} - 6$ .

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Step 1.1.1

Factor $2$ out of $8 w$ .

$\frac{2 (4 w) - 2 w^{2} - 6}{w - 1}$

Step 1.1.2

Factor $2$ out of $- 2 w^{2}$ .

$\frac{2 (4 w) + 2 (- w^{2}) - 6}{w - 1}$

Step 1.1.3

Factor $2$ out of $- 6$ .

$\frac{2 (4 w) + 2 (- w^{2}) + 2 (- 3)}{w - 1}$

Step 1.1.4

Factor $2$ out of $2 (4 w) + 2 (- w^{2})$ .

$\frac{2 (4 w - w^{2}) + 2 (- 3)}{w - 1}$

Step 1.1.5

Factor $2$ out of $2 (4 w - w^{2}) + 2 (- 3)$ .

$\frac{2 (4 w - w^{2} - 3)}{w - 1}$

Step 1.2

Let $u = w$ . Substitute $u$ for all occurrences of $w$ .

$\frac{2 (4 u - u^{2} - 3)}{w - 1}$

Step 1.3

Factor by grouping.

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Step 1.3.1

Reorder terms.

$\frac{2 (- u^{2} + 4 u - 3)}{w - 1}$

Step 1.3.2

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 $a \cdot c = - 1 \cdot - 3 = 3$ and whose sum is $b = 4$ .

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Step 1.3.2.1

Factor $4$ out of $4 u$ .

$\frac{2 (- u^{2} + 4 (u) - 3)}{w - 1}$

Step 1.3.2.2

Rewrite $4$ as $1$ plus $3$

$\frac{2 (- u^{2} + (1 + 3) u - 3)}{w - 1}$

Step 1.3.2.3

Apply the distributive property.

$\frac{2 (- u^{2} + 1 u + 3 u - 3)}{w - 1}$

Step 1.3.2.4

Multiply $u$ by $1$ .

$\frac{2 (- u^{2} + u + 3 u - 3)}{w - 1}$

Step 1.3.3

Factor out the greatest common factor from each group.

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Step 1.3.3.1

Group the first two terms and the last two terms.

$\frac{2 ((- u^{2} + u) + 3 u - 3)}{w - 1}$

Step 1.3.3.2

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

$\frac{2 (u (- u + 1) - 3 (- u + 1))}{w - 1}$

Step 1.3.4

Factor the polynomial by factoring out the greatest common factor, $- u + 1$ .

$\frac{2 ((- u + 1) (u - 3))}{w - 1}$

Step 1.4

Replace all occurrences of $u$ with $w$ .

$\frac{2 (- w + 1) (w - 3)}{w - 1}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $- w + 1$ and $w - 1$ .

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Step 2.1.1

Factor $- 1$ out of $- w$ .

$\frac{2 (- (w) + 1) (w - 3)}{w - 1}$

Step 2.1.2

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{2 (- (w) - 1 (- 1)) (w - 3)}{w - 1}$

Step 2.1.3

Factor $- 1$ out of $- (w) - 1 (- 1)$ .

$\frac{2 (- (w - 1)) (w - 3)}{w - 1}$

Step 2.1.4

Rewrite $- (w - 1)$ as $- 1 (w - 1)$ .

$\frac{2 (- 1 (w - 1)) (w - 3)}{w - 1}$

Step 2.1.5

Cancel the common factor.

$\frac{2 (- 1 (w - 1)) (w - 3)}{w - 1}$

Step 2.1.6

Divide $2 \cdot (- 1) (w - 3)$ by $1$ .

$2 \cdot (- 1) (w - 3)$

Step 2.2

Multiply $2$ by $- 1$ .

$- 2 (w - 3)$

Step 2.3

Apply the distributive property.

$- 2 w - 2 \cdot - 3$

Step 2.4

Multiply $- 2$ by $- 3$ .

$- 2 w + 6$