SOLUTION: Please help me solve this problem: Siplify: {{{ ((1/(1-x))+(x/(x-1))) / ((1/(1-x))-(x/(x-1))) }}} I know that i have to find a least common multiple but i don't know how to

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Please help me solve this problem: Siplify: {{{ ((1/(1-x))+(x/(x-1))) / ((1/(1-x))-(x/(x-1))) }}} I know that i have to find a least common multiple but i don't know how to      Log On


   

Question 68071: Please help me solve this problem:
Siplify:

I know that i have to find a least common multiple but i don't know how to finish it.
Thank you very much!!!


Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
You need to get rid of the denominators in the smaller individual fractions. This will make the overall expression easier to deal with.

multiply by (1-x)

multiply by (x-1)
+%28%28x-1%29%2B%28x%281-x%29%29%29+%2F+%28%28x-1%29-%28x%281-x%29%29%29+
Now expand the brackets
+%28%28x-1%29%2B%28x-x%5E2%29%29+%2F+%28%28x-1%29-%28x-x%5E2%29%29+
Simplify
+%28-x%5E2%2B2x-1%29+%2F+%28-x%5E2-1%29
If you try and simplify this any further you may find the bottom term is hard to factorise, because you will need to use the square root of a negative number