Divide (x^2-49)/(7-x)

$\frac{x^{2} - 49}{7 - x}$

Step 1

Simplify the numerator.

Rewrite $49$ as $7^{2}$ .

$\frac{x^{2} - 7^{2}}{7 - x}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 7$ .

$\frac{(x + 7) (x - 7)}{7 - x}$

Step 2

Cancel the common factor of $x - 7$ and $7 - x$ .

Factor $- 1$ out of $x$ .

$\frac{(x + 7) (- 1 (- x) - 7)}{7 - x}$

Rewrite $- 7$ as $- 1 (7)$ .

$\frac{(x + 7) (- 1 (- x) - 1 (7))}{7 - x}$

Factor $- 1$ out of $- 1 (- x) - 1 (7)$ .

$\frac{(x + 7) (- 1 (- x + 7))}{7 - x}$

Reorder terms.

$\frac{(x + 7) (- 1 (- x + 7))}{- x + 7}$

Cancel the common factor.

$\frac{(x + 7) (- 1 (- x + 7))}{- x + 7}$

Divide $(x + 7) \cdot (- 1)$ by $1$ .

$(x + 7) \cdot (- 1)$

Step 3

Apply the distributive property.

$x \cdot - 1 + 7 \cdot - 1$

Step 4

Move $- 1$ to the left of $x$ .

$- 1 \cdot x + 7 \cdot - 1$

Step 5

Multiply $7$ by $- 1$ .

$- 1 \cdot x - 7$

Step 6

Rewrite $- 1 x$ as $- x$ .

$- x - 7$