Find the difference: $$ \frac{x+1}{x-1}-\frac{x-8}{x-1} $$

Question

UpStudy AI · Accepted Answer

1. Start with the expression:
   $$
   \frac{x+1}{x-1}-\frac{x-8}{x-1}
   $$

2. Since the denominators are the same ($$x-1$$), combine the fractions:
   $$
   \frac{(x+1) - (x-8)}{x-1}
   $$

3. Distribute the negative sign in the numerator:
   $$
   (x+1)-(x-8) = x + 1 - x + 8
   $$

4. Combine like terms:
   $$
   x - x + 1 + 8 = 9
   $$

5. Substitute back into the fraction:
   $$
   \frac{9}{x-1}
   $$

Thus, the difference is:
$$
\frac{9}{x-1}
$$
The difference is $$ \frac{9}{x-1} $$.

Find the difference: \( \frac{x+1}{x-1}-\frac{x-8}{x-1} \)