Expert: Josh - 1/14/2009

Question
a/a-1/a-a/1-a
=a/a-1/a-a^2-a/1-a
=a/a-1/-a^2
=a/a-1-a/a^2
=a/a+1-a/a^2
=a/a^3+1-a/a
=a*a^2/a^3-a+1
=a^3/a^3-a+1
Hey please explain the avobe example step by step.please explain each step.


Answer
Surya

You have to understand that it is VERY difficult to read any expression involving fractions when you type it in a single line without using brackets. Something like a-1/a-2 can be interpreted in several ways: it could be three separate terms given by a - (1/a) - 2, OR two terms given by [(a-1)/a] - 2, OR a single fraction (a-1)/(a-2).

I will try to disambiguate this starting at the bottom.

=(a/a^3)+1-(a/a) ...find lowest common denominator to combine fractions
                   note: the following line does not seem to follow,
                   I think (if I understand this line correctly) the
                   next line should be (a-a^2)/a^3 - a + 1
=(a*a^2)/a^3-a+1 ...multiply to simplify product in the numerator
=(a^3/a^3)-a+1

This is not going to work....there is no hope of following these steps unless we get the syntax right (with the use of brackets from the very first line) so that each expression can be properly understood.