Question

Simplify the expression 2x/x²​ ÷ x−2​/2x ÷ 2/x−1​ and state the result in its simplest form when x is not equal to -2, 1.

Answer 1

To simplify the expression, divide each fraction separately and then combine the fractions using division and multiplication.

Step-by-step explanation:

To simplify the expression 2x/x² ÷ x−2/2x ÷ 2/x−1,

1. First, simplify each fraction separately:
   • 2x/x² simplifies to 2/x
   • x−2/2x simplifies to 1/(2x)
   • 2/x−1 simplifies to 2/(x-1)
2. Next, divide the fractions:
   • 2/x ÷ 1/(2x) is the same as multiplying 2/x by 2x/1, which simplifies to 4
   • 4 ÷ 2/(x-1) is the same as multiplying 4 by (x-1)/2, which simplifies to 2(x-1)

Therefore, the simplified expression is 2(x-1).