Simplified expression of 1- ^2 y 1+ y + 1+ y y - y 1- y is

Step-by-step solution

The given expression is E = 1 - ² y 1 + y + 1 + y y - y 1 - y . Using the identity ² y = 1 - ² y = (1 - y)(1 + y) , the second term simplifies as: ² y 1 + y = (1 - y)(1 + y) 1 + y = 1 - y . Substituting this into the expression: E = 1 - (1 - y) + 1 + y y - y 1 - y E = y + 1 + y y - y 1 - y . Combine the last two terms by taking the common denominator y (1 - y) : (1 + y)(1 - y) - ² y y (1 - y) = 1 - ² y - ² y y (1 - y) . Since ² y + ² y = 1 , the numerator becomes 1 - ( ² y + ² y) = 1 - 1 = 0 . Therefore, E = y + 0