Trigonometry Examples

$\frac{a^{- 1} + 1}{a^{- 1} - 1}$

Step 1

Set the denominator in $\frac{a^{- 1} + 1}{a^{- 1} - 1}$ equal to $0$ to find where the expression is undefined.

$a^{- 1} - 1 = 0$

Step 2

Solve for $a$ .

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Step 2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{a} - 1 = 0$

Step 2.2

Add $1$ to both sides of the equation.

$\frac{1}{a} = 1$

Step 2.3

Find the LCD of the terms in the equation.

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Step 2.3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$a, 1$

Step 2.3.2

The LCM of one and any expression is the expression.

$a$

Step 2.4

Multiply each term in $\frac{1}{a} = 1$ by $a$ to eliminate the fractions.

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Step 2.4.1

Multiply each term in $\frac{1}{a} = 1$ by $a$ .

$\frac{1}{a} a = 1 a$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $a$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{1}{a} a = 1 a$

Step 2.4.2.1.2

Rewrite the expression.

$1 = 1 a$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Multiply $a$ by $1$ .

$1 = a$

Step 2.5

Rewrite the equation as $a = 1$ .

$a = 1$

Step 3

Set the base in $a^{- 1}$ equal to $0$ to find where the expression is undefined.

$a = 0$

Step 4

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$a = 0, a = 1$

Step 5