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
\(\frac{4x}{x^2-9}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\frac{1}{x-3}-\frac{3(x-1)}{x^2 - 9}\)
\(\frac{1}{x-3}-\frac{3(x-1)}{(x-3)(x+3)}\)
\(\frac{x+3-3x+3}{(x-3)(x+3)};\frac{-2x+6}{(x-3)(x+3)}\)
\(\frac{-2(x-3)}{(x-3)(x+3)}=\frac{-2}{x+3}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #26454)