The root(s) of 15/(x2 - 4) – 2/(x - 2) = 1 is (are):
Correct answer: A
Explanation
15/(x2 - 4) – 2/(x - 2) = 1.
15/(x2 - 22) – 2/(x - 2) = 1.
15/(x + 2)(x - 2) – 2/(x - 2) = 1.
[15 – 2(x + 2)]/[(x + 2)(x - 2)] = 1.
[15 – 2x - 4] /[(x + 2)(x - 2)] = 1.
[11 - 2x]/[(x + 2)(x - 2)] = 1.
11 – 2x = (x + 2)(x - 2).
11 – 2x = x2 - 4.
x2 - 4 = 11 – 2x.
x2 + 2x – 4 – 11 = 0.
x2 + 2x – 15 = 0.
x + 5) (x - 3) = 0.
x + 5 = 0 or, x – 3 = 0
x = -5 or, x = 3.
Therefore, x = -5 and 3.
A
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