Question

Which expression is equivalent to (2 + 2/x) / (4 - 4/x)? Assume x ≠ 0 and x ≠ 1. a) (2 + x/2) b) (x + 2/x) c) (2 - 2/x) d) (x/2 + 2)

Answer 1

To simplify the given expression (2 + 2/x) / (4 - 4/x), we can find a common denominator, factor out common terms, and cancel out the common factor to get (x + 1) / (2x - 2).

Step-by-step explanation:

To simplify the expression (2 + 2/x) / (4 - 4/x), we can start by finding a common denominator for the numerator and the denominator. The common denominator is x, so we multiply the numerator and the denominator by x to get (2x + 2) / (4x - 4).

Next, we can factor out a 2 from both the numerator and the denominator to get 2(x + 1) / 2(2x - 2).

Finally, we can cancel out the common factor of 2 to simplify the expression to (x + 1) / (2x - 2).

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