Simplify (x+1)/(x-1)-(x-8)/(x-1)

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Simplify each term.

Apply the distributive property.

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

Multiply $- 1$ by $- 8$ .

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

Step 3

Simplify by adding terms.

Combine the opposite terms in $x + 1 - x + 8$ .

Subtract $x$ from $x$ .

$\frac{0 + 1 + 8}{x - 1}$

Add $0$ and $1$ .

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

Add $1$ and $8$ .

$\frac{9}{x - 1}$