Simplify \(\frac{1}{x-3}-\frac{3(x-1)}{x^2 - 9}\)
MATHEMATICS
WAEC 2000
Simplify \(\frac{1}{x-3}-\frac{3(x-1)}{x^2 - 9}\)
- A. \(\frac{x-1}{x-3}\)
- B. \(\frac{-2}{x+3}\)
- C. \(\frac{x-1}{x+3}\)
- D. \(\frac{4x}{x^2-9}\)
Correct Answer: B. \(\frac{-2}{x+3}\)
Explanation
\(\frac{1}{x-3}-\frac{3(x-1)}{x^2 - 9}\\
\frac{1}{x-3}-\frac{3(x-1)}{(x-3)(x+3)}\\
\frac{x+3-3x+3}{(x-3)(x+3)};\frac{-2x+6}{(x-3)(x+3)}\\
\frac{-2(x-3)}{(x-3)(x+3)}=\frac{-2}{x+3}\)
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