Express \(\frac{2}{x + 3} - \frac{1}{x - 2}\) as a simple fraction
A
\(\frac{x - 7}{x^2 + x - 6}\)
B
\(\frac{x - 1}{x^2 + x - 6}\)
C
\(\frac{x - 2}{x^2 + x - 6}\)
D
\(\frac{x - 27}{x^2 + x - 6}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\frac{2}{x + 3} - \frac{1}{x - 2}\) = \(\frac{2(x - 2) - (x - 3)}{(x + 3) (x - 2)}\)
= \(\frac{2x - 4 - x - 3}{x^2 - 2x + 3x - 6}\)
= \(\frac{x -7}{x^2 + x - 6}\)
= \(\frac{x - 7}{x^2 + x - 6}\)
Source: Myschool Past Questions Archive (Record #36896)