Question

subtract.
\\(\frac{6}{x} - \frac{5}{x + 1}\\)
simplify your answer as much as possible.

Explanation:

Step1: Find common denominator

The common denominator of \( \frac{6}{x} \) and \( \frac{5}{x + 1} \) is \( x(x + 1) \). Rewrite each fraction:
\( \frac{6}{x}=\frac{6(x + 1)}{x(x + 1)}=\frac{6x+6}{x(x + 1)} \)
\( \frac{5}{x + 1}=\frac{5x}{x(x + 1)} \)

Step2: Subtract the fractions

Subtract the numerators: \( \frac{6x + 6-5x}{x(x + 1)} \)

Step3: Simplify the numerator

Simplify \( 6x + 6-5x \) to get \( x + 6 \). So the result is \( \frac{x + 6}{x(x + 1)} \)

Answer:

\( \frac{x + 6}{x(x + 1)} \)