SOLUTION: My question is the proper steps to simplify this equation: ((x)/(1-x)) - ((y)/(1-y)) The book's answer is: ((x-y)/(xy-x-y+1)) I got to the middle step, ((x(1-y)

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Question 937688: My question is the proper steps to simplify this equation:
((x)/(1-x)) - ((y)/(1-y))
The book's answer is:
((x-y)/(xy-x-y+1))
I got to the middle step,
((x(1-y) - (y(1-x) / (1-x)(1-y))
That's where I get lost.
Any help is appreciated!
Thanks
Found 3 solutions by josgarithmetic, MathLover1, rothauserc:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website!
Your "middle step" should be expressed as this:

PERFORM THE INDICATED OPERATIONS and simplifications for the numerator! Just that first part-step will first become this:

Keep going and finish.

Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
the middle step is correct,
...now just do multiplication in numerator and denominator

Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website!
((x)/(1-x)) - ((y)/(1-y))
use (1-x)*(1-y) as the common denominator, then
x(1-y) - y(1-x) / (1-x)(1-y)
(x-xy - y +xy) / (1-x)(1-y)
(x-y) / (1-x)(1-y)
((x-y)/(xy-x-y+1))

SOLUTION: My question is the proper steps to simplify this equation: ((x)/(1-x)) - ((y)/(1-y)) The book's answer is: ((x-y)/(xy-x-y+1)) I got to the middle step, ((x(1-y) - (y(1