Simplify 5/(2(x-4)^2-6)

$\frac{5}{2 {(x - 4)}^{2} - 6}$

Step 1

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

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

$\frac{5}{2 ({(x - 4)}^{2}) - 6}$

Factor $2$ out of $- 6$ .

$\frac{5}{2 {(x - 4)}^{2} + 2 \cdot - 3}$

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

$\frac{5}{2 ({(x - 4)}^{2} - 3)}$

Step 2

Rewrite ${(x - 4)}^{2}$ as $(x - 4) (x - 4)$ .

$\frac{5}{2 ((x - 4) (x - 4) - 3)}$

Step 3

Expand $(x - 4) (x - 4)$ using the FOIL Method.

Apply the distributive property.

$\frac{5}{2 (x (x - 4) - 4 (x - 4) - 3)}$

Apply the distributive property.

$\frac{5}{2 (x \cdot x + x \cdot - 4 - 4 (x - 4) - 3)}$

Apply the distributive property.

$\frac{5}{2 (x \cdot x + x \cdot - 4 - 4 x - 4 \cdot - 4 - 3)}$

Step 4

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$\frac{5}{2 (x^{2} + x \cdot - 4 - 4 x - 4 \cdot - 4 - 3)}$

Move $- 4$ to the left of $x$ .

$\frac{5}{2 (x^{2} - 4 \cdot x - 4 x - 4 \cdot - 4 - 3)}$

Multiply $- 4$ by $- 4$ .

$\frac{5}{2 (x^{2} - 4 x - 4 x + 16 - 3)}$

Subtract $4 x$ from $- 4 x$ .

$\frac{5}{2 (x^{2} - 8 x + 16 - 3)}$

Step 5

Subtract $3$ from $16$ .

$\frac{5}{2 (x^{2} - 8 x + 13)}$