Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $a - 1$ and $1 - a$ .

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Step 1.1.1

Factor $- 1$ out of $a$ .

$\frac{- 1 (- a) - 1}{1 - a} + \frac{1 - b}{b - 1}$

Step 1.1.2

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

$\frac{- 1 (- a) - 1 (1)}{1 - a} + \frac{1 - b}{b - 1}$

Step 1.1.3

Factor $- 1$ out of $- 1 (- a) - 1 (1)$ .

$\frac{- 1 (- a + 1)}{1 - a} + \frac{1 - b}{b - 1}$

Step 1.1.4

Reorder terms.

$\frac{- 1 (- a + 1)}{- a + 1} + \frac{1 - b}{b - 1}$

Step 1.1.5

Cancel the common factor.

$\frac{- 1 (- a + 1)}{- a + 1} + \frac{1 - b}{b - 1}$

Step 1.1.6

Divide $- 1$ by $1$ .

$- 1 + \frac{1 - b}{b - 1}$

Step 1.2

Cancel the common factor of $1 - b$ and $b - 1$ .

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Step 1.2.1

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

$- 1 + \frac{- 1 (- 1) - b}{b - 1}$

Step 1.2.2

Factor $- 1$ out of $- b$ .

$- 1 + \frac{- 1 (- 1) - (b)}{b - 1}$

Step 1.2.3

Factor $- 1$ out of $- 1 (- 1) - (b)$ .

$- 1 + \frac{- 1 (- 1 + b)}{b - 1}$

Step 1.2.4

Reorder terms.

$- 1 + \frac{- 1 (b - 1)}{b - 1}$

Step 1.2.5

Cancel the common factor.

$- 1 + \frac{- 1 (b - 1)}{b - 1}$

Step 1.2.6

Divide $- 1$ by $1$ .

$- 1 - 1$

Step 2

Subtract $1$ from $- 1$ .

$- 2$