Precalculus Examples

$\frac{{(b - 2)}^{2}}{{(2 - b)}^{2}}$

Step 1

Set the denominator in $\frac{{(b - 2)}^{2}}{{(2 - b)}^{2}}$ equal to $0$ to find where the expression is undefined.

${(2 - b)}^{2} = 0$

Step 2

Solve for $b$ .

Tap for more steps...

Step 2.1

Set the $2 - b$ equal to $0$ .

$2 - b = 0$

Step 2.2

Solve for $b$ .

Tap for more steps...

Step 2.2.1

Subtract $2$ from both sides of the equation.

$- b = - 2$

Step 2.2.2

Divide each term in $- b = - 2$ by $- 1$ and simplify.

Tap for more steps...

Step 2.2.2.1

Divide each term in $- b = - 2$ by $- 1$ .

$\frac{- b}{- 1} = \frac{- 2}{- 1}$

Step 2.2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{b}{1} = \frac{- 2}{- 1}$

Step 2.2.2.2.2

Divide $b$ by $1$ .

$b = \frac{- 2}{- 1}$

Step 2.2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.2.3.1

Divide $- 2$ by $- 1$ .

$b = 2$

Step 3

The domain is all values of $b$ that make the expression defined.

Interval Notation:

$(- \infty, 2) \cup (2, \infty)$

Set-Builder Notation:

${b | b \neq 2}$

Step 4