Final answer:
To simplify the expression (2-(x+1)/(x))/(3+(x-1)/(x+1)), start by simplifying the numerator and denominator separately. Then combine like terms in the numerator and denominator. Finally, substitute the simplified expressions back into the original expression.
Step-by-step explanation:
To simplify the expression (2-(x+1)/(x))/(3+(x-1)/(x+1)), we can start by simplifying the numerator and denominator separately. For the numerator, we distribute the negative sign to the terms inside the parentheses: 2 - (x/x + 1/x). This simplifies to: 2 - (1 + 1/x). For the denominator, we distribute the positive sign to the terms inside the parentheses: 3 + (x/x + 1/x + 1/(x+1)). This simplifies to: 3 + (1 + 1/x + 1/(x+1)).
Next, we combine like terms in the numerator and denominator. The numerator becomes: 2 - 1 - 1/x = 1 - 1/x. The denominator becomes: 3 + 1 + 1/x + 1/(x+1) = 4 + 1/x + 1/(x+1).
Finally, we substitute these simplified expressions back into the original expression to get: (1 - 1/x)/(4 + 1/x + 1/(x+1)). This is the simplified form of the expression.