Finite Math Examples

$\frac{5}{x - 1} - \frac{x - 2}{1 - x}$

Step 1

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

$\frac{5}{x - 1} - \frac{x - 2}{- 1 (- 1) - x}$

Step 2

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

$\frac{5}{x - 1} - \frac{x - 2}{- 1 (- 1) - (x)}$

Step 3

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

$\frac{5}{x - 1} - \frac{x - 2}{- 1 (- 1 + x)}$

Step 4

Reorder terms.

$\frac{5}{x - 1} - \frac{x - 2}{- 1 (x - 1)}$

Step 5

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

$\frac{5}{x - 1} \cdot \frac{- 1}{- 1} - \frac{x - 2}{- 1 (x - 1)}$

Step 6

Write each expression with a common denominator of $(x - 1) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{5}{x - 1}$ by $\frac{- 1}{- 1}$ .

$\frac{5 \cdot - 1}{(x - 1) \cdot - 1} - \frac{x - 2}{- 1 (x - 1)}$

Step 6.2

Reorder the factors of $(x - 1) \cdot - 1$ .

$\frac{5 \cdot - 1}{- (x - 1)} - \frac{x - 2}{- 1 (x - 1)}$

Step 7

Combine the numerators over the common denominator.

$\frac{5 \cdot - 1 - (x - 2)}{- (x - 1)}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $5$ by $- 1$ .

$\frac{- 5 - (x - 2)}{- (x - 1)}$

Step 8.2

Apply the distributive property.

$\frac{- 5 - x - - 2}{- (x - 1)}$

Step 8.3

Multiply $- 1$ by $- 2$ .

$\frac{- 5 - x + 2}{- (x - 1)}$

Step 8.4

Add $- 5$ and $2$ .

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

Step 9

Simplify with factoring out.

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Step 9.1

Move the negative in front of the fraction.

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

Step 9.2

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

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

Step 9.3

Rewrite $- 3$ as $- 1 (3)$ .

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

Step 9.4

Factor $- 1$ out of $- (x) - 1 (3)$ .

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

Step 9.5

Simplify the expression.

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Step 9.5.1

Rewrite $- (x + 3)$ as $- 1 (x + 3)$ .

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

Step 9.5.2

Move the negative in front of the fraction.

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

Step 9.5.3

Multiply $- 1$ by $- 1$ .

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

Step 9.5.4

Multiply $\frac{x + 3}{x - 1}$ by $1$ .

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