If pq + 1 = q2 and t = 1p 1 p - 1pq 1 p q express t in terms of q

Question 1 Report

If pq + 1 = q2 and t = $\frac{1}{p}$ - $\frac{1}{p q}$ express t in terms of q

1

P-Q

1

q-1

1

q+1

1 + q

1

1-q

Answer Details

Pq + 1 = q2......(i)
t = $\frac{1}{p}$ - $\frac{1}{p q}$ .........(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 = $\frac{q - 1}{q^{2} - 1}$
= $\frac{q - 1}{(q + 1) (q - 1)}$
= $\frac{1}{q + 1}$

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