Problem: If 10x−1a+10x+2b=(10x−1)(10x+2)2⋅10x+3 is an identity for positive rational values of x, then the value of a−b is:
Answer Choices:
A. 4/3
B. 5/3
C. 2
D. 11/4
E. 3
Solution:
a(10x+2)+b(10x−1)=2⋅10x+3∴a+b=2 and 2a−b=3∴a=35 and b=31∴a−b=34.