Basic Math Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Factor $v$ out of $4 (3 - v) (2 v) - v^{2} \cdot - 4$ .

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Step 1.1.1

Factor $v$ out of $4 (3 - v) (2 v)$ .

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

Step 1.1.2

Factor $v$ out of $- v^{2} \cdot - 4$ .

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

Step 1.1.3

Factor $v$ out of $v (4 (3 - v) \cdot (2)) + v (- v \cdot - 4)$ .

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Multiply $4$ by $3$ .

$\frac{v ((12 + 4 (- v)) \cdot 2 - v \cdot - 4)}{4 {(3 - v)}^{2}}$

Step 1.4

Multiply $- 1$ by $4$ .

$\frac{v ((12 - 4 v) \cdot 2 - v \cdot - 4)}{4 {(3 - v)}^{2}}$

Step 1.5

Apply the distributive property.

$\frac{v (12 \cdot 2 - 4 v \cdot 2 - v \cdot - 4)}{4 {(3 - v)}^{2}}$

Step 1.6

Multiply $12$ by $2$ .

$\frac{v (24 - 4 v \cdot 2 - v \cdot - 4)}{4 {(3 - v)}^{2}}$

Step 1.7

Multiply $2$ by $- 4$ .

$\frac{v (24 - 8 v - v \cdot - 4)}{4 {(3 - v)}^{2}}$

Step 1.8

Multiply $- 4$ by $- 1$ .

$\frac{v (24 - 8 v + 4 v)}{4 {(3 - v)}^{2}}$

Step 1.9

Add $- 8 v$ and $4 v$ .

$\frac{v (24 - 4 v)}{4 {(3 - v)}^{2}}$

Step 1.10

Factor $4$ out of $24 - 4 v$ .

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Step 1.10.1

Factor $4$ out of $24$ .

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

Step 1.10.2

Factor $4$ out of $- 4 v$ .

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

Step 1.10.3

Factor $4$ out of $4 (6) + 4 (- v)$ .

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

$\frac{v \cdot 4 (6 - v)}{4 {(3 - v)}^{2}}$

Step 2

Cancel the common factor of $4$ .

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Step 2.1

Cancel the common factor.

$\frac{v \cdot 4 (6 - v)}{4 {(3 - v)}^{2}}$

Step 2.2

Rewrite the expression.

$\frac{v (6 - v)}{{(3 - v)}^{2}}$