If pq + 1 = q2 and t = (frac{1}{p}) – (frac{1}{pq}) express t in terms of q
-
A.
(frac{1}{p – q}) -
B.
(frac{1}{q – 1}) -
C.
(frac{1}{q + 1}) -
D.
1 + 0 -
E.
(frac{1}{1 – q})
Correct Answer: Option C
Explanation
Pq + 1 = q2……(i)
t = (frac{1}{p}) – (frac{1}{pq})………(ii)
p = (frac{q^2 – 1}{q})
Sub for p in equation (ii)
t = (frac{1}{q^2 – frac{1}{q}}) – (frac{1}{frac{q^2 – 1}{q} times q})
t = (frac{q}{q^2 – 1}) – (frac{1}{q^2 – 1})
t = (frac{q – 1}{q^2 – 1})
= (frac{q – 1}{(q + 1)(q – 1)})
= (frac{1}{q + 1})