Problem: The expression a+yy​−a−ya​a+ya​+a−yy​​, a real, aî€ =0, has the value −1 for:
Answer Choices:
A. all but two real values of y
B. only two real values of y
C. all real values of y
D. only one real value of y
E. no real values of y
Solution:
To avoid division by zero, yî€ =a and yî€ =−a. With these values excluded we may simplify the fraction by multiplying numerator and denominator by (a+y)(a−y), obtaining ay−y2−a2−aya2−ay+ay+y2​=−(a2+y2)a2+y2​=−1