Question 30385
If the answer should be a/(1-a), then the problem should be
[(1/a) + 1)] / [(1/a2) - 1)]
=[(1 + a)/a] divided by  [(1-a^2)/a^2]
= [(1 + a)/a] X  a^2/(1-a^2)
= [(1 + a)/a] X  a^2/[(1+a)(1-a)]
=[a^2(1+a)]/[a(1+a)(1-a)]  (multiplying nr by nr and dr by dr)
= a/(1-a)  (cancelling a(1+a) )
Answer: a/(1-a)


And for the given problem (1/a + 1) / (1/a2 - 1)
the steps are as follows:
[1/(a + 1)]divided by[1/(a2 - 1)]
= [1/(a + 1)]divided by {1/[(a+1)(a-1)]}
= [1/(a + 1)]multiplied by [(a+1)(a-1)]/1 
= [1/(a + 1)]X [(a+1)(a-1)]/1 
=(a-1)
Answer: (a-1)

(when you replace a division symbol by the multiplication symbol the fraction that comes after the division symbol should be reciprocated that is the new fraction near the multiplication symbol should be 1/(old fraction) )