Simplify ((4t^2-16)/8)/((t-2)/6)

$\frac{\frac{4 t^{2} - 16}{8}}{\frac{t - 2}{6}}$

Step 1

Cancel the common factor of $4 t^{2} - 16$ and $8$ .

Factor $4$ out of $4 t^{2}$ .

$\frac{\frac{4 (t^{2}) - 16}{8}}{\frac{t - 2}{6}}$

Factor $4$ out of $- 16$ .

$\frac{\frac{4 t^{2} + 4 \cdot - 4}{8}}{\frac{t - 2}{6}}$

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

$\frac{\frac{4 (t^{2} - 4)}{8}}{\frac{t - 2}{6}}$

Cancel the common factors.

Factor $4$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{\frac{t^{2} - 4}{2}}{\frac{t - 2}{6}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{t^{2} - 4}{2} \cdot \frac{6}{t - 2}$

Step 3

Simplify terms.

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

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

Cancel the common factor.

$\frac{t^{2} - 4}{2} \cdot \frac{2 \cdot 3}{t - 2}$

Rewrite the expression.

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

Multiply $t^{2} - 4$ by $\frac{3}{t - 2}$ .

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

Step 4

Simplify the numerator.

Rewrite $4$ as $2^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = t$ and $b = 2$ .

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

Step 5

Simplify terms.

Cancel the common factor of $t - 2$ .

Cancel the common factor.

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

Divide $(t + 2) \cdot 3$ by $1$ .

$(t + 2) \cdot 3$

Apply the distributive property.

$t \cdot 3 + 2 \cdot 3$

Simplify the expression.

Move $3$ to the left of $t$ .

$3 \cdot t + 2 \cdot 3$

Multiply $2$ by $3$ .

$3 t + 6$

Simplify ((4t^2-16)/8)/((t-2)/6)

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