Question

find the difference:
\\(\frac{x + 1}{x - 1} - \frac{x - 8}{x - 1}\\)
options:
\\(\frac{2x + 9}{x - 1}\\)
\\(\frac{-7}{x - 1}\\)
\\(\frac{2x - 7}{x - 1}\\)
\\(\frac{9}{x - 1}\\)

Explanation:

Step1: Subtract the numerators

Since the denominators are the same ($x - 1$), we subtract the numerators: $(x + 1) - (x - 8)$.
$$(x + 1) - (x - 8) = x + 1 - x + 8$$

Step2: Simplify the numerator

Simplify the expression from Step 1: $x + 1 - x + 8 = 9$.

Step3: Write the result

The denominator remains $x - 1$, so the result is $\frac{9}{x - 1}$.

Answer:

$\frac{9}{x - 1}$ (corresponding to the option with $\frac{9}{x - 1}$)