find the difference:\n$\frac{x + 1}{x - 1}-\frac{x - 8}{x - 1}$\n$\frac{9}{x - 1}$\n$\frac{2x - 7}{x…

find the difference:\n$\frac{x + 1}{x - 1}-\frac{x - 8}{x - 1}$\n$\frac{9}{x - 1}$\n$\frac{2x - 7}{x - 1}$\n$\frac{-7}{x - 1}$\n$\frac{2x + 9}{x - 1}$\ndone

find the difference:\n$\frac{x + 1}{x - 1}-\frac{x - 8}{x - 1}$\n$\frac{9}{x - 1}$\n$\frac{2x - 7}{x - 1}$\n$\frac{-7}{x - 1}$\n$\frac{2x + 9}{x - 1}$\ndone

Answer

Explanation:

Step1: Combine the fractions

Since the denominators are the same ($x - 1$), we subtract the numerators: $\frac{(x + 1)-(x - 8)}{x - 1}$.

Step2: Simplify the numerator

Expand the numerator: $(x+1)-(x - 8)=x + 1-x + 8$. Combine like - terms: $x-x+1 + 8=9$. So the fraction is $\frac{9}{x - 1}$.

Answer:

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