Question

Which expression is equivalent to the following complex tion?

[(y+1)(y-1)/2 ÷ y+1/y-1]

A. (y-1)/2)

B. (y+1/y-1)

C. (y-1/y+1)

D. (y+1)(y-1)/2)

Answer 1

The equivalent expression to the given fraction [(y+1)(y-1)/2 ÷ (y+1)/(y-1)] is (y-1)/2 by canceling out common terms in the numerator and the denominator.

Step-by-step explanation:

To find the expression equivalent to the complex fraction [(y+1)(y-1)/2 ÷ (y+1)/(y-1)], we need to follow a step-by-step process. First, understand the operation: division of fractions is the same as multiplication by the reciprocal. So, re-write the expression by keeping the first fraction and multiplying by the reciprocal of the second:

[(y+1)(y-1)/2] × [(y-1)/(y+1)]

Next, simplify by canceling out terms that appear both in the numerator and the denominator. The terms (y+1) in the first fraction's numerator and the second fraction's denominator cancel each other out. Similarly, the (y-1) terms cancel out:

[(y-1)/2]

Therefore, the equivalent expression to the given complex fraction is option A: (y-1)/2.