If p = (frac{1}{2}) and (frac{1}{p – 1} = frac{2}{p + x}), find the value of x
-
A.
-2(frac{1}{2}) -
B.
-1(frac{1}{2}) -
C.
1(frac{1}{2}) -
D.
2(frac{1}{2})
Correct Answer: Option B
Explanation
p = (frac{1}{2}; frac{1}{p – 1} = frac{2}{p + x})
(frac{1}{frac{1}{2} – 1} = frac{2}{frac{1}{2} + x})
(frac{1}{frac{1 – 2}{2}} = frac{2}{frac{1 + 2x}{2}})
(frac{1}{-frac{1}{2}} = frac{2}{frac{1 + 2x}{2}})
-2 = (frac{4}{1 + 2x} -2(1 + 2x) = 4)
1 + 2x = (frac{4}{-2})
1 + 2x = -2
2x = -2 – 1
2x = -3
x = -(frac{3}{2})
x = -1(frac{1}{2})