Algebra Examples

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

Step 1

Simplify terms.

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Step 1.1

Factor $2$ out of $4 k - 2$ .

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Step 1.1.1

Factor $2$ out of $4 k$ .

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

Step 1.1.2

Factor $2$ out of $- 2$ .

$\frac{k + 3}{2 (2 k) + 2 (- 1)} \cdot (12 k^{2} - 3)$

Step 1.1.3

Factor $2$ out of $2 (2 k) + 2 (- 1)$ .

$\frac{k + 3}{2 (2 k - 1)} \cdot (12 k^{2} - 3)$

Step 1.2

Multiply $\frac{k + 3}{2 (2 k - 1)}$ by $12 k^{2} - 3$ .

$\frac{(k + 3) (12 k^{2} - 3)}{2 (2 k - 1)}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $3$ out of $12 k^{2} - 3$ .

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Step 2.1.1

Factor $3$ out of $12 k^{2}$ .

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

Step 2.1.2

Factor $3$ out of $- 3$ .

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

Step 2.1.3

Factor $3$ out of $3 (4 k^{2}) + 3 (- 1)$ .

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

Step 2.2

Rewrite $4 k^{2}$ as ${(2 k)}^{2}$ .

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

Step 2.3

Rewrite $1$ as $1^{2}$ .

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

Step 2.4

Factor.

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

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $2 k - 1$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

$\frac{(k + 3) \cdot 3 (2 k + 1)}{2}$

Step 3.2

Move $3$ to the left of $k + 3$ .

$\frac{3 (k + 3) (2 k + 1)}{2}$