How would I solve this?
G(x) = 1 / x where x = 1, x = a
So far i've gotten to :
(1 / a - 1 / 1) / a - 1
But after that i'm completely stuck..... help someone!!
I explained several methods here, check them out. get back to me if you are not clear
i find that the last method i used in my last post is most useful when figuring out the LCD is a pain, or when dealing with algebra involving a lot of variables.
The first line that you worked, wouldn't the result from
1 / a - 1 / 1 =
1 - a? Because you would have to find the common denominator and that being (a), the (a) would cancel out and leave 1 and for the second term, 1/1 = 1 so it'll simply be 1 x a which is a. The whole problem would be
(1 - a) / a - 1
Am i wrong? if so could you tell me why?
yes you are wrong. You can only cancel things that way in a fraction when you have a single term in the numerator and denominator. this means we have to have a product or division of terms for that to work.
(1 - a) are two terms. we separate terms using +'s and -'s. we cannot cancel the a without affecting the 1 in this case, and therefore, what you did was incorrect. if it was a(1 - a)/a then we could cancel the a's, since we have one term in the top and bottom, yes a(1 - a) is considered to be ONE term, since it is a product
no, you should ask questions! i think everyone here likes that, it shows that you are not just after answers but are really trying to understand what is going on, which is refreshing.
i noticed that $\displaystyle 1 - a = -(a - 1)$
and we have an $\displaystyle a - 1$ in the denominator. since we have one term in the numerator and the denominator, i can cancel the like terms. so i cancel the $\displaystyle a - 1$ in the top and bottom, but it was a minus $\displaystyle a - 1$ in the top, so i had to leave the minus sign there, so i ended up with $\displaystyle - \frac {1}{a}$