Precalculus Examples

$\frac{3}{x - 1} - 5$

Step 1

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{x - 1}{x - 1}$ .

$\frac{3}{x - 1} - 5 \cdot \frac{x - 1}{x - 1}$

Step 2

Simplify terms.

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Step 2.1

Combine $- 5$ and $\frac{x - 1}{x - 1}$ .

$\frac{3}{x - 1} + \frac{- 5 (x - 1)}{x - 1}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{3 - 5 (x - 1)}{x - 1}$

Step 3

Simplify the numerator.

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Step 3.1

Apply the distributive property.

$\frac{3 - 5 x - 5 \cdot - 1}{x - 1}$

Step 3.2

Multiply $- 5$ by $- 1$ .

$\frac{3 - 5 x + 5}{x - 1}$

Step 3.3

Add $3$ and $5$ .

$\frac{- 5 x + 8}{x - 1}$

Step 4

Simplify with factoring out.

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Step 4.1

Factor $- 1$ out of $- 5 x$ .

$\frac{- (5 x) + 8}{x - 1}$

Step 4.2

Rewrite $8$ as $- 1 (- 8)$ .

$\frac{- (5 x) - 1 (- 8)}{x - 1}$

Step 4.3

Factor $- 1$ out of $- (5 x) - 1 (- 8)$ .

$\frac{- (5 x - 8)}{x - 1}$

Step 4.4

Simplify the expression.

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Step 4.4.1

Rewrite $- (5 x - 8)$ as $- 1 (5 x - 8)$ .

$\frac{- 1 (5 x - 8)}{x - 1}$

Step 4.4.2

Move the negative in front of the fraction.

$- \frac{5 x - 8}{x - 1}$