Precalculus Examples

$\frac{1 + \frac{9}{c - 1}}{1 - \frac{9}{c - 1}}$

Step 1

Multiply the numerator and denominator of the fraction by $c - 1$ .

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Step 1.1

Multiply $\frac{1 + \frac{9}{c - 1}}{1 - \frac{9}{c - 1}}$ by $\frac{c - 1}{c - 1}$ .

$\frac{c - 1}{c - 1} \cdot \frac{1 + \frac{9}{c - 1}}{1 - \frac{9}{c - 1}}$

Step 1.2

Combine.

$\frac{(c - 1) (1 + \frac{9}{c - 1})}{(c - 1) (1 - \frac{9}{c - 1})}$

Step 2

Apply the distributive property.

$\frac{(c - 1) \cdot 1 + (c - 1) \frac{9}{c - 1}}{(c - 1) \cdot 1 + (c - 1) (- \frac{9}{c - 1})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $c - 1$ .

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Step 3.1.1

Cancel the common factor.

$\frac{(c - 1) \cdot 1 + (c - 1) \frac{9}{c - 1}}{(c - 1) \cdot 1 + (c - 1) (- \frac{9}{c - 1})}$

Step 3.1.2

Rewrite the expression.

$\frac{(c - 1) \cdot 1 + 9}{(c - 1) \cdot 1 + (c - 1) (- \frac{9}{c - 1})}$

Step 3.2

Cancel the common factor of $c - 1$ .

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Step 3.2.1

Move the leading negative in $- \frac{9}{c - 1}$ into the numerator.

$\frac{(c - 1) \cdot 1 + 9}{(c - 1) \cdot 1 + (c - 1) \frac{- 9}{c - 1}}$

Step 3.2.2

Cancel the common factor.

$\frac{(c - 1) \cdot 1 + 9}{(c - 1) \cdot 1 + (c - 1) \frac{- 9}{c - 1}}$

Step 3.2.3

Rewrite the expression.

$\frac{(c - 1) \cdot 1 + 9}{(c - 1) \cdot 1 - 9}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $c - 1$ by $1$ .

$\frac{c - 1 + 9}{(c - 1) \cdot 1 - 9}$

Step 4.2

Add $- 1$ and $9$ .

$\frac{c + 8}{(c - 1) \cdot 1 - 9}$

Step 5

Simplify the denominator.

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Step 5.1

Multiply $c - 1$ by $1$ .

$\frac{c + 8}{c - 1 - 9}$

Step 5.2

Subtract $9$ from $- 1$ .

$\frac{c + 8}{c - 10}$