Simplify 8/(4(x-3)^2-5)

$\frac{8}{4 {(x - 3)}^{2} - 5}$

Step 1

Rewrite ${(x - 3)}^{2}$ as $(x - 3) (x - 3)$ .

$\frac{8}{4 ((x - 3) (x - 3)) - 5}$

Step 2

Expand $(x - 3) (x - 3)$ using the FOIL Method.

Apply the distributive property.

$\frac{8}{4 (x (x - 3) - 3 (x - 3)) - 5}$

Apply the distributive property.

$\frac{8}{4 (x \cdot x + x \cdot - 3 - 3 (x - 3)) - 5}$

Apply the distributive property.

$\frac{8}{4 (x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3) - 5}$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$\frac{8}{4 (x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3) - 5}$

Move $- 3$ to the left of $x$ .

$\frac{8}{4 (x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3) - 5}$

Multiply $- 3$ by $- 3$ .

$\frac{8}{4 (x^{2} - 3 x - 3 x + 9) - 5}$

Subtract $3 x$ from $- 3 x$ .

$\frac{8}{4 (x^{2} - 6 x + 9) - 5}$

Step 4

Apply the distributive property.

$\frac{8}{4 x^{2} + 4 (- 6 x) + 4 \cdot 9 - 5}$

Step 5

Simplify.

Multiply $- 6$ by $4$ .

$\frac{8}{4 x^{2} - 24 x + 4 \cdot 9 - 5}$

Multiply $4$ by $9$ .

$\frac{8}{4 x^{2} - 24 x + 36 - 5}$

Step 6

Subtract $5$ from $36$ .

$\frac{8}{4 x^{2} - 24 x + 31}$