Yessica...hello from ABQ
I understand your problem 2-x/1-x/2 to be ( 2 - x )/( 1 - x/2) In words, the quantity 2 minus 2 divided by the quantity 1 minus x over 2... correct? When these responses get sent, then don't always look like we are invisioning them...so I'll use words as well as numbers...)to begin with, our numerator 2 - x (two minus x) over the denominator 1 - x over 2 (1 - x/2)
the numerator 1 -x can be left alone for now...we will have to deal with the denominator first.
We have as the denominator 1 - x/2. When subtracting fractions, the denominators have to be the same, right. we will have to change the 1 to a fraction so that it has a denominator of 2 because of the x/2. So we have to find the LCD...least common denominator for the 1 and the x/2, in this case it is 2, so now we have 2/2 - x/2 (do you see how that was done? 2 over 2 is the same as one, correct, now we have the same like terms as denominators.) Now combine the two fractions together, with the numerator being 2 - x and the denominators being 2...now the bottom fraction becomes (2 - x)/2.
Now combine it with the original equation: (2-x)/(1-x/2) which becomes
(2 - x)/ (2 - x)/2 or (2 - x) divided by (2 - x)/2 Since we're dividing fractions we change the division sign to multiplication which becomes (2 - x) times (2 - x)/2 or (2 - x) x (2 - x)/2 sorry if the too many x's get confusing. After we change the signs, we invert the second term to 2 / (2 - x) do you see that? Our new equation becomes
(2 - x) times 2 /(2 - x) the numerator of the equation is (2 - x) and the denominator is 2 over (2 - x). Notice we have the quantity (2 - x) as the numerator and for the (2 - x) as the denominator. Since they are like terms, they cancel out, and now we have 1 x 2 which equals 2. I know that reading it is difficult to visualize, especially when this format doesn't allow to show it completely. If you're still confused, respond to my answer, and we'll see about helping you understand these kinds of problems. As your read each step...write it down on a paper, which will give you a visual picture. Good luck