SOLUTION: (1/a + 1) / (1/a2 - 1) The book gives an answer as: a/1-a, but I just can't see how they get it. You must first multiply both numerator and denominator by the LCD, right? Isn

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: (1/a + 1) / (1/a2 - 1) The book gives an answer as: a/1-a, but I just can't see how they get it. You must first multiply both numerator and denominator by the LCD, right? Isn      Log On


   

Question 30385: (1/a + 1) / (1/a2 - 1)
The book gives an answer as: a/1-a, but I just can't see how they get it.
You must first multiply both numerator and denominator by the LCD, right? Isn't this 2a? When I multiply both by it, I get:
(2 + 2a) / (1 - 2a)
and get stuck there. What am I doing wrong?
Found 2 solutions by longjonsilver, sdmmadam@yahoo.com:
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
Assuming you mean: +%28+1%2F%28a%2B1%29+%29+%2F+%28+1%2F%28a%5E2-1%29+%29+, we get:
+%28+1%2F%28a%2B1%29+%29+%2A+%28+%28a%5E2-1%29%2F1+%29+
+%28a%5E2-1%29%2F%28a%2B1%29+
+%28%28a-1%29%28a%2B1%29%29%2F%28a%2B1%29+
+%28a-1%29+

As for the answer you quote, a/(a-1), I cannot see how that was gotten, from the starting point i used.

jon.

Answer by sdmmadam@yahoo.com(530) About Me  (Show Source):
You can put this solution on YOUR website!
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) )