Problem:
How many pairs (a,b) of non-zero real numbers satisfy the equation
a1​+b1​=a+b1​?
Answer Choices:
A. none
B. 1
C. 2
D. one pair for each bî€ =0
E. two pairs for each bî€ =0
Solution:
The given equation is equivalent to each of these equations
aba+b​(a+b)2a2+ab+b2​=a+b1​=ab=0.​
Since the last equation is satisfied by the pairs (a,b) such that a=2−b±−3b2​​, there are no pairs of real numbers satisfying the original equation.