Home » If pq + 1 = q2 and t = (frac{1}{p}) – (frac{1}{pq}) express t in…

If pq + 1 = q2 and t = (frac{1}{p}) – (frac{1}{pq}) express t in…

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})