Simplify (x^2-121)/(11-x)

$\frac{x^{2} - 121}{11 - x}$

Step 1

Simplify the numerator.

Rewrite $121$ as $11^{2}$ .

$\frac{x^{2} - 11^{2}}{11 - x}$

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 $b = 11$ .

$\frac{(x + 11) (x - 11)}{11 - x}$

Step 2

Simplify terms.

Cancel the common factor of $x - 11$ and $11 - x$ .

Factor $- 1$ out of $x$ .

$\frac{(x + 11) (- 1 (- x) - 11)}{11 - x}$

Rewrite $- 11$ as $- 1 (11)$ .

$\frac{(x + 11) (- 1 (- x) - 1 (11))}{11 - x}$

Factor $- 1$ out of $- 1 (- x) - 1 (11)$ .

$\frac{(x + 11) (- 1 (- x + 11))}{11 - x}$

Reorder terms.

$\frac{(x + 11) (- 1 (- x + 11))}{- x + 11}$

Cancel the common factor.

$\frac{(x + 11) (- 1 (- x + 11))}{- x + 11}$

Divide $(x + 11) \cdot (- 1)$ by $1$ .

$(x + 11) \cdot (- 1)$

Simplify by multiplying through.

Apply the distributive property.

$x \cdot - 1 + 11 \cdot - 1$

Simplify the expression.

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

$- 1 \cdot x + 11 \cdot - 1$

Multiply $11$ by $- 1$ .

$- 1 \cdot x - 11$

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

$- x - 11$