SOLUTION: Well I thought I understood polynomials until I got to the rational expressions aspect of them. For example how do I solve: ab - a + b - 1 / ab + a + b + 1 I believe the first

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Well I thought I understood polynomials until I got to the rational expressions aspect of them. For example how do I solve: ab - a + b - 1 / ab + a + b + 1 I believe the first       Log On


   

Question 244618: Well I thought I understood polynomials until I got to the rational expressions aspect of them. For example how do I solve:
ab - a + b - 1 / ab + a + b + 1
I believe the first step is to factor out ab, but I'm lost after that. The answer given in back of book is:
b - 1 / b + 1
But can't the b's be factored out as well since they are equal?
Thank you in advance.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28ab-a%2Bb-1%29%2F%28ab+%2B+a+%2B+b+%2B+1+%29 Start with the given expression.


%28a%28b-1%29%2Bb-1%29%2F%28ab+%2B+a+%2B+b+%2B+1+%29 Factor an 'a' out of the terms ab-a in the numerator.


%28a%28b-1%29%2Bb-1%29%2F%28a%28b+%2B+1%29+%2B+b+%2B+1+%29 Factor an 'a' out of the terms ab%2Ba in the denominator.



%28%28b-1%29%28a%2B1%29%29%2F%28%28b+%2B+1%29%28a%2B1%29%29 Factor out the GCF b-1 in the numerator. Factor out the GCF b%2B1 in the denominator.



%28%28b-1%29highlight%28%28a%2B1%29%29%29%2F%28%28b+%2B+1%29highlight%28%28a%2B1%29%29%29 Highlight the common terms.


%28%28b-1%29cross%28%28a%2B1%29%29%29%2F%28%28b+%2B+1%29cross%28%28a%2B1%29%29%29 Cancel out the common terms.


%28b-1%29%2F%28b%2B1%29 Simplify.


From here, no more simplification can be done. So you can't factor out the 'b's


So %28ab-a%2Bb-1%29%2F%28ab+%2B+a+%2B+b+%2B+1+%29=%28b-1%29%2F%28b%2B1%29