Simplify ((x+3)/(x+1)-2)/(x-1)

$\frac{\frac{x + 3}{x + 1} - 2}{x - 1}$

Step 1

Multiply the numerator and denominator of the complex fraction by $x + 1$ .

Multiply $\frac{\frac{x + 3}{x + 1} - 2}{x - 1}$ by $\frac{x + 1}{x + 1}$ .

$\frac{x + 1}{x + 1} \cdot \frac{\frac{x + 3}{x + 1} - 2}{x - 1}$

Combine.

$\frac{(x + 1) (\frac{x + 3}{x + 1} - 2)}{(x + 1) (x - 1)}$

Step 2

Apply the distributive property.

$\frac{(x + 1) \frac{x + 3}{x + 1} + (x + 1) \cdot - 2}{(x + 1) x + (x + 1) \cdot - 1}$

Step 3

Cancel the common factor of $x + 1$ .

Cancel the common factor.

$\frac{(x + 1) \frac{x + 3}{x + 1} + (x + 1) \cdot - 2}{(x + 1) x + (x + 1) \cdot - 1}$

Rewrite the expression.

$\frac{x + 3 + (x + 1) \cdot - 2}{(x + 1) x + (x + 1) \cdot - 1}$

Step 4

Simplify the numerator.

Apply the distributive property.

$\frac{x + 3 + x \cdot - 2 + 1 \cdot - 2}{(x + 1) x + (x + 1) \cdot - 1}$

Move $- 2$ to the left of $x$ .

$\frac{x + 3 - 2 \cdot x + 1 \cdot - 2}{(x + 1) x + (x + 1) \cdot - 1}$

Multiply $- 2$ by $1$ .

$\frac{x + 3 - 2 \cdot x - 2}{(x + 1) x + (x + 1) \cdot - 1}$

Subtract $2 x$ from $x$ .

$\frac{- x + 3 - 2}{(x + 1) x + (x + 1) \cdot - 1}$

Subtract $2$ from $3$ .

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

Step 5

Simplify terms.

Factor $x + 1$ out of $(x + 1) x + (x + 1) \cdot - 1$ .

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

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

Factor $x + 1$ out of $(x + 1) \cdot - 1$ .

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

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

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

Cancel the common factor of $- x + 1$ and $x - 1$ .

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

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

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

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

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Simplify ((x+3)/(x+1)-2)/(x-1)

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