Simplify 7/(2(x-6)^2-4)

$\frac{7}{2 {(x - 6)}^{2} - 4}$

Factor $2$ out of $2 {(x - 6)}^{2} - 4$ .

Factor $2$ out of $2 {(x - 6)}^{2}$ .

$\frac{7}{2 ({(x - 6)}^{2}) - 4}$

Factor $2$ out of $- 4$ .

$\frac{7}{2 {(x - 6)}^{2} + 2 \cdot - 2}$

Factor $2$ out of $2 {(x - 6)}^{2} + 2 \cdot - 2$ .

$\frac{7}{2 ({(x - 6)}^{2} - 2)}$

Rewrite ${(x - 6)}^{2}$ as $(x - 6) (x - 6)$ .

$\frac{7}{2 ((x - 6) (x - 6) - 2)}$

Expand $(x - 6) (x - 6)$ using the FOIL Method.

Apply the distributive property.

$\frac{7}{2 (x (x - 6) - 6 (x - 6) - 2)}$

Apply the distributive property.

$\frac{7}{2 (x \cdot x + x \cdot - 6 - 6 (x - 6) - 2)}$

Apply the distributive property.

$\frac{7}{2 (x \cdot x + x \cdot - 6 - 6 x - 6 \cdot - 6 - 2)}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$\frac{7}{2 (x^{2} + x \cdot - 6 - 6 x - 6 \cdot - 6 - 2)}$

Move $- 6$ to the left of $x$ .

$\frac{7}{2 (x^{2} - 6 \cdot x - 6 x - 6 \cdot - 6 - 2)}$

Multiply $- 6$ by $- 6$ .

$\frac{7}{2 (x^{2} - 6 x - 6 x + 36 - 2)}$

Subtract $6 x$ from $- 6 x$ .

$\frac{7}{2 (x^{2} - 12 x + 36 - 2)}$

Subtract $2$ from $36$ .

$\frac{7}{2 (x^{2} - 12 x + 34)}$