Simplifying Complex Fractions: A Step-by-Step Guide with Example

Which expression is equivalent to the following complex fraction?(1 + 1/y) / (1 – 1/y)

B.

To simplify the given complex fraction, we can use the following steps:

Step 1: Find a common denominator for the numerator and denominator of the complex fraction. The common denominator in this case is y, so we can rewrite the complex fraction as:

[(y + 1)/y] / [(y – 1)/y]

Step 2: Invert the denominator and multiply by the numerator. This is the same as flipping the second fraction and multiplying it by the first. The expression then simplifies as:

[(y + 1)/y] * [y/(y – 1)]

Step 3: Simplify the expression. We can cancel the factors of y in the numerator and denominator of the first fraction, and we can also factor out a 1 from the second fraction. The expression then simplifies as:

(y + 1) / (y – 1)

Therefore, the expression equivalent to the complex fraction (1 + 1/y) / (1 – 1/y) is (y + 1) / (y – 1).

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