Divide ((x-4)^2)/((x-9)^2)

$\frac{{(x - 4)}^{2}}{{(x - 9)}^{2}}$

Step 1

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

$\frac{(x - 4) (x - 4)}{{(x - 9)}^{2}}$

Step 2

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

Apply the distributive property.

$\frac{x (x - 4) - 4 (x - 4)}{{(x - 9)}^{2}}$

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

$\frac{x^{2} - 4 \cdot x - 4 x - 4 \cdot - 4}{{(x - 9)}^{2}}$

Multiply $- 4$ by $- 4$ .

$\frac{x^{2} - 4 x - 4 x + 16}{{(x - 9)}^{2}}$

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

$\frac{x^{2} - 8 x + 16}{{(x - 9)}^{2}}$

Step 4

Split the fraction $\frac{x^{2} - 8 x + 16}{{(x - 9)}^{2}}$ into two fractions.

$\frac{x^{2} - 8 x}{{(x - 9)}^{2}} + \frac{16}{{(x - 9)}^{2}}$

Step 5

Split the fraction $\frac{x^{2} - 8 x}{{(x - 9)}^{2}}$ into two fractions.

$\frac{x^{2}}{{(x - 9)}^{2}} + \frac{- 8 x}{{(x - 9)}^{2}} + \frac{16}{{(x - 9)}^{2}}$

Step 6

Move the negative in front of the fraction.

$\frac{x^{2}}{{(x - 9)}^{2}} - \frac{8 x}{{(x - 9)}^{2}} + \frac{16}{{(x - 9)}^{2}}$